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  • 1
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    Editorial: Flank dynamics, sector collapses, lahars, and rockfalls: analysis, monitoring, and modelling of small to large scale volcanic slope instability (2020)
    Springer
    Details
    Publication Date: 2020-11-12
    Description: Slope dynamics in volcanic environments comprise a wide spectrum of phenomena, from large lateral collapse to shallow debris remobilization, which may represent a major threat for human communities and infrastructures. Many volcanos built up from the ocean floor and large portions of the volcano edifice are submerged. In these settings, only the edifice’s summit can be investigated by terrestrial remote sensing and in-situ approaches. Growth and destruction, including tectonics and gravitational phenomena, affect entire volcano flanks and are not limited to the physical boundary of the sea level but could comprise their subaqueous parts.
    Description: Published
    Description: 2615–2618
    Description: 6V. Pericolosità vulcanica e contributi alla stima del rischio
    Description: JCR Journal
    Keywords: volcanoes ; flanks ; volcano-tectonics ; structure ; collapse ; stability ; 04.08. Volcanology ; 05.08. Risk
    Repository Name: Istituto Nazionale di Geofisica e Vulcanologia (INGV)
    Type: article
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  • 2
    Electronic Resource
    Electronic Resource
    Existence and stability of equilibria in age-structured population dynamics (1984)
    Springer
    Journal of mathematical biology 20 (1984), S. 259-276 
    Details
    ISSN: 1432-1416
    Keywords: Age-structured population dynamics ; equilibria ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275988
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  • 3
    Electronic Resource
    Electronic Resource
    Predator-prey relationships: Indiscriminate predation (1984)
    Springer
    Journal of mathematical biology 21 (1984), S. 25-34 
    Details
    ISSN: 1432-1416
    Keywords: Predator-prey ; density dependence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Gurtin and Levine model5 is studied in this paper under the assumption that the fecundity of prey depends on age as well as on the total population sizes of prey and predators. The purpose of this study is to see the effect of this density dependence on the stability criteria for the equilibria of the model equations. It is shown that there are cases when, due to density dependence, the model which is originally neutrally stable becomes stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275220
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  • 4
    Electronic Resource
    Electronic Resource
    Persistence, stability and level crossings in an integrodifferential system (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 395-426 
    Details
    ISSN: 1432-1416
    Keywords: Uniform persistence ; stability ; Lyapunov functional ; level-crossing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Dynamical characteristics of an integrodifferential system modelling two species competition with hereditary effects are investigated; in particular we derive sufficient conditions for the persistence of the species, existence of an attracting periodic solution and ‘level-crossings’ of solutions about the periodic solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160166
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  • 5
    Electronic Resource
    Electronic Resource
    Single-locus gametophytic incompatibility: the symmetric equilibrium is globally asymptotically stable (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 515-520 
    Details
    ISSN: 1432-1416
    Keywords: Gametophytic incompatibility ; model ; equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The deterministic dynamics of the classical single-locus multiple-allele model of gametophytic incompatibility is analyzed with the intention to prove the conjecture that the symmetric state (uniform distribution of genotypes) is the only polymorphic equilibrium and that this equilibrium is globally asymptotically stable in the interior of the frequency simplex. It is shown that the minimum allelic frequency increases strictly over the generations as long as a uniform allelic distribution is not realized. Hence, the minimum allelic frequency is a Ljapunov function for the invariant set of genotypic frequencies characterized by a uniform allelic distribution. Within this set, the uniform genotypic distribution is approached in an exponential fashion, which proves the assertion. An evolutionary optimization rule associated with the global convergence to the symmetric state is implied by the fact that at this state the overall amount of pollen elimination resulting from incompatible crosses is minimized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00573457
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  • 6
    Electronic Resource
    Electronic Resource
    Permanent coexistence in general models of three interacting species (1985)
    Springer
    Journal of mathematical biology 21 (1985), S. 285-298 
    Details
    ISSN: 1432-1416
    Keywords: Population dynamics ; coexistence ; mutualism ; persistence ; predator-mediated coexistence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x i = X i f i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276227
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  • 7
    Electronic Resource
    Electronic Resource
    Stability of fast travelling pulse solutions of the FitzHugh—Nagumo equations (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 81-104 
    Details
    ISSN: 1432-1416
    Keywords: FitzHugh-Nagumo equation ; pulse solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The FitzHugh-Nagumo equation u t =u xx +f(u)-w, u t =b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b〉0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b〉0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d〉0, and is “marginally stable” but not exponentially stable if d=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276548
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  • 8
    Electronic Resource
    Electronic Resource
    A generalization of the Nash equilibrium theorem on bimatrix games (1996)
    Springer
    International journal of game theory 25 (1996), S. 1-12 
    Details
    ISSN: 1432-1270
    Keywords: Bimatrix game ; ɛ-equilibrium ; optimal strategies ; vertical linear complementarity problem ; degree ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this article, we consider a two-person game in which the first player picks a row representative matrixM from a nonempty set $$A$$ ofm ×n matrices and a probability distributionx on {1,2,...,m} while the second player picks a column representative matrixN from a nonempty set ℬ ofm ×n matrices and a probability distribution y on 1,2,...,n. This leads to the respective costs ofx t My andx t Ny for these players. We establish the existence of an ɛ-equilibrium for this game under the assumption that $$A$$ and ℬ are bounded. When the sets $$A$$ and ℬ are compact in ℝmxn, the result yields an equilibrium state at which stage no player can decrease his cost by unilaterally changing his row/column selection and probability distribution. The result, when further specialized to singleton sets, reduces to the famous theorem of Nash on bimatrix games.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01254380
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  • 9
    Electronic Resource
    Electronic Resource
    A note on multiple flow equilibria (1989)
    Springer
    Pure and applied geophysics 130 (1989), S. 743-749 
    Details
    ISSN: 1420-9136
    Keywords: Dynamic systems ; multiple equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A set of ordinary differential equations describing a mechanical system subject to forcing and dissipation is considered. A topological argument is employed to show that if all time-dependent solutions of the governing equations are bounded, the equations admitN steady solutions, whereN is a positive odd integer and where at least (N−1)/2 of the steady solutions are unstable. The results are discussed in the context of atmospheric flows, and it is shown that truncated forms of the quasigeostrophic equations of dynamic meteorology and of Budyko-Sellers climate models satisfy the hypotheses of the theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00881609
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  • 10
    Electronic Resource
    Electronic Resource
    A catastrophe analysis on the stability of the crack growth in three-point bending specimens (1996)
    Springer
    Acta mechanica solida Sinica 9 (1996), S. 179-183 
    Details
    ISSN: 0894-9166
    Keywords: crack growth ; stability ; cusp catastrophe ; J-integral ; three-point bending specimen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper presents an attempt at the application of catastrophe theory to the stability analysis ofJ-controlled crack growth in three-point bending specimens. By introducing the solutions ofJ- integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02209162
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