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  • 1
    Electronic Resource
    Electronic Resource
    A New ADI Scheme for Solving Three-Dimensional Parabolic Equations with First-Order Derivatives and Variable Coefficients (2000)
    Springer
    Journal of computational analysis and applications 2 (2000), S. 293-308 
    Details
    ISSN: 1572-9206
    Keywords: parabolic equations ; ADI scheme ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1010108620966
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  • 2
    Electronic Resource
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    Bifurcation Phenomena from Standing Pulse Solutions in Some Reaction-Diffusion Systems (2000)
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 117-167 
    Details
    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009098719440
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  • 3
    Electronic Resource
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    Stability of Linear Inequality Systems Measured by the Hausdorff Metric (2000)
    Springer
    Set-valued analysis 8 (2000), S. 253-266 
    Details
    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008701026782
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  • 4
    Electronic Resource
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    Stability Properties of a Bond Portfolio Management Problem (2000)
    Springer
    Annals of operations research 99 (2000), S. 251-265 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019275817688
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  • 5
    Electronic Resource
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    Destabilization for quasivariational inequalities of reaction-diffusion type (2000)
    Springer
    Applications of mathematics 45 (2000), S. 161-176 
    Details
    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023033910657
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  • 6
    Electronic Resource
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    Diagonally implicit Runge–Kutta methods for 3D shallow water applications (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 229-250 
    Details
    ISSN: 1572-9044
    Keywords: numerical analysis ; shallow water problems ; DIRK methods ; stability ; 65L06 ; 65L20 ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018969203026
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  • 7
    Electronic Resource
    Electronic Resource
    On the Robustness of Gaussian Elimination with Partial Pivoting (2000)
    Springer
    BIT 40 (2000), S. 62-73 
    Details
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; pivoting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022314201484
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  • 8
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    Runge-Kutta Methods for the Numerical Solution of Stiff Semilinear Systems (2000)
    Springer
    BIT 40 (2000), S. 611-639 
    Details
    ISSN: 1572-9125
    Keywords: Runge-Kutta methods ; stability ; convergence ; stiff problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022332200092
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  • 9
    Electronic Resource
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    Stochastic Methods for Ill-Posed Problems (2000)
    Springer
    BIT 40 (2000), S. 226-240 
    Details
    ISSN: 1572-9125
    Keywords: Stochastic differential equations ; regularisation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022386822865
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  • 10
    Electronic Resource
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    Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 313-320 
    Details
    ISSN: 1573-0530
    Keywords: partial differential equations ; nonlinearities ; symmetries ; stability ; minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007622208894
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  • 11
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    On the Stability of Functional Equations and a Problem of Ulam (2000)
    Springer
    Acta applicandae mathematicae 62 (2000), S. 23-130 
    Details
    ISSN: 1572-9036
    Keywords: stability ; functional equations ; Cauchy difference ; semigroup ; inequalities ; approximate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006499223572
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  • 12
    Electronic Resource
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    Numerical solutions for a coupled non-linear oscillator (2000)
    Springer
    Journal of mathematical chemistry 28 (2000), S. 325-340 
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    ISSN: 1572-8897
    Keywords: numerical method ; stability ; Hopf bifurcation ; coupled oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A second-order accurate numerical method has been proposed for the solution of a coupled non-linear oscillator featuring in chemical kinetics. Although implicit by construction, the method enables the solution of the model initial-value problem (IVP) to be computed explicitly. The second-order method is constructed by taking a linear combination of first-order methods. The stability analysis of the system suggests the existence of a Hopf bifurcation, which is confirmed by the numerical method. Both the critical point of the continuous system and the fixed point of the numerical method will be seen to have the same stability properties. The second-order method is more competitive in terms of numerical stability than some well-known standard methods (such as the Runge–Kutta methods of order two and four).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011025104111
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  • 13
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    Stability and chaotic motion in columns of nonlinear viscoelastic material (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 987-994 
    Details
    ISSN: 1573-2754
    Keywords: stability ; chaos ; averaging method ; Galerkin method ; viscoelastic column ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459307
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  • 14
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    Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1177-1186 
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    ISSN: 1573-2754
    Keywords: elastic foundation ; pipe conveying fluid ; coupled-mode flutter ; stability ; power series method ; 0353
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method. Compared with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio β, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458996
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  • 15
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    Research on stability of moving jet containing dense suspended solid particles (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1390-1400 
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    ISSN: 1573-2754
    Keywords: suspended solid particles ; continuum phase-coupled model ; stability ; moving jet ; numerical computation ; O359
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet for different downstream distances, Reynolds number of flow-field, particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme. Founded on the analysis of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field but the effect of the negative one is contrary. In addition, particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field. These conclusions benefit learning the development of moving two-phase jet.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459217
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  • 16
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    Analysis and calculation of the nonlinear stability of the rotational composite shell (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 209-216 
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    ISSN: 1573-2754
    Keywords: composite material ; rotational shell ; stability ; nonlinear ; O347.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract By adopting the energy method, a new method to calculate the stability of the composite shell of revolution is presented. This method takes the influence of nonlinear prebuckling deformations and stresses on the buckling of the shell into account. The relationships between the prebuckling deformations and strains are calculated by nonlinear Kármán equations. The numerical method is used to calculate the energy of the total system. The nonlinear equations are solved by combining gradient method and amendatory Newton iterative method. The computer program is also developed. An example is given to demonstrate the accuracy of the method presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458522
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  • 17
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    Convergence and stability of recursive damped least square algorithm (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 237-242 
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    ISSN: 1573-2754
    Keywords: system identification ; damped least square ; recursive algorithm ; convergence ; stability ; O231 ; O241
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458525
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  • 18
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    Mixed Solutions for Weak Stackelberg Problems: Existence and Stability Results (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 417-440 
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    ISSN: 1573-2878
    Keywords: mixed solutions ; weak Stackelberg problems ; existence ; stability ; weak convergence of probability measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We are concerned with ∈-mixed solutions for weak Stackelberg problems corresponding to two-player nonzero-sum noncooperative games. Two cases are considered: (i) mixed strategies for only the second player; (ii) mixed strategies for both players. After giving basic results relating convergence of functions and weak convergence of probability measures, we establish existence and stability results for ∈-mixed solutions under general assumptions of minimal character without any convexity assumption. Our results improve previous work of Mallozzi and Morgan (Refs. 1–2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004618103646
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  • 19
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    Optimal Dynamic Investment Policy for Different Tax Depreciation Rates and Economic Depreciation Rates (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 23-48 
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    ISSN: 1573-2878
    Keywords: Optimal control ; investment policy ; tax depreciation ; economic depreciation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper analyzes the investment policy consequences of incorporating a tax depreciation rate different from the economic depreciation rate. Most often, firms choose their tax depreciation rate in a strategic way. Therefore, it would be a coincidence, should the optimization process lead to a tax depreciation rate that equals the economic depreciation rate. The implications of a difference between tax depreciation rate and economic depreciation rate are investigated in an optimal control model for the determination of the firm investment policy over time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004650906179
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  • 20
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    Optimum Radius of Robust Stability for Schur Polynomials (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 165-174 
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    ISSN: 1573-2878
    Keywords: Systems theory ; stability ; robust stability ; linear systems ; discrete-time systems ; robustness ; polynomial theory ; Kharitonov theorem ; inverse Kharitonov problem ; Rouche theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper investigates the problem of the robust stability of Schur polynomials. Recently, a new approach based on the Rouche theorem of classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of the previous solution is presented. This is the optimum solution of the robust stability problem for Schur polynomials, which is obtained by solving a minimization problem and is better than other methods in robust stability literature. Three numerical examples are given to illustrate the proposed method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004684907724
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  • 21
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    Extended Well-Posedness Properties of Vector Optimization Problems (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 165-182 
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    ISSN: 1573-2878
    Keywords: Vector optimization ; asymptotically minimizing sequences ; extended well-posedness ; stability ; vector variational principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004615325743
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  • 22
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    On the Robust Stability of 2D Schur Polynomials (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 431-439 
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    ISSN: 1573-2878
    Keywords: multidimensional polynomial theory ; robustness ; Kharitonov theorem ; stability ; Schur polynomials ; inverse Kharitonov problem ; Rouché theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note, the problem of the robust stability for a two-dimensional (two-variable) Schur polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem is adopted. The extension to the robust stability for multidimensional (multivariable) polynomials is also provided. Interesting sufficient conditions for such robust stability are derived. A two-dimensional example is included to support the theoretical result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004615917160
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  • 23
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    Upper and Lower Semicontinuity for Set-Valued Mappings Involving Constraints (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 527-550 
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    ISSN: 1573-2878
    Keywords: vector optimization ; set-valued mappings ; constraint sets ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In vector optimization, several authors have studied the upper and lower semicontinuity for mappings involving constraints in topological vector spaces partially ordered through a cone with nonempty interior. In this paper, we give conditions about the upper and lower semicontinuity in the case that the ordering cone in the parameter space has possibly empty interior, as it happens in many function spaces and seqence spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004653312019
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  • 24
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    Deterministic Global Optimization in Nonlinear Optimal Control Problems (2000)
    Springer
    Journal of global optimization 17 (2000), S. 97-126 
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    ISSN: 1573-2916
    Keywords: Differential-algebraic equations ; Global optimization ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The accurate solution of optimal control problems is crucial in many areas of engineering and applied science. For systems which are described by a nonlinear set of differential-algebraic equations, these problems have been shown to often contain multiple local minima. Methods exist which attempt to determine the global solution of these formulations. These algorithms are stochastic in nature and can still get trapped in local minima. There is currently no deterministic method which can solve, to global optimality, the nonlinear optimal control problem. In this paper a deterministic global optimization approach based on a branch and bound framework is introduced to address the nonlinear optimal control problem to global optimality. Only mild conditions on the differentiability of the dynamic system are required. The implementa-tion of the approach is discussed and computational studies are presented for four control problems which exhibit multiple local minima.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026578104213
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  • 25
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    Stability and Hopf Bifurcation of Four-Wheel-Steering Vehicles Involving Driver's Delay (2000)
    Springer
    Nonlinear dynamics 22 (2000), S. 361-374 
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    ISSN: 1573-269X
    Keywords: 4WS vehicle ; time delay ; stability ; Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A mathematical model is presented for four-wheel-steeringvehicles, with the time delay in driver's response and the nonlinearityin lateral tyre forces taken into account. It is proved that thevehicle-driver system has a trivial steady state motion, as well aseight non-trivial steady state motions due to the nonlinearity of tyreforces. The asymptotic stability and Hopf bifurcation of the trivialsteady state are analyzed for two control strategies ofrear-wheel-steering. It is shown through the numerical simulations thatthe four-wheel-steering technique based on the bilinear control strategyworks better when the driver's response involves time delay.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008324311249
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