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  • 1
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    Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu–Wang Four-Wing Chaotic System (2020)
    Hindawi
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    Publication Date: 2020-08-29
    Description: In this paper, we further study the dynamic characteristics of the Yu–Wang chaotic system obtained by Yu and Wang in 2012. The system can show a four-wing chaotic attractor in any direction, including all 3D spaces and 2D planes. For this reason, our interest is focused on multistability generation and chaotic FPGA implementation. The stability analysis, bifurcation diagram, basin of attraction, and Lyapunov exponent spectrum are given as the methods to analyze the dynamic behavior of this system. The analyses show that each system parameter has different coexistence phenomena including coexisting chaotic, coexisting stable node, and coexisting limit cycle. Some remarkable features of the system are that it can generate transient one-wing chaos, transient two-wing chaos, and offset boosting. These phenomena have not been found in previous studies of the Yu–Wang chaotic system, so they are worth sharing. Then, the RK4 algorithm of the Verilog 32-bit floating-point standard format is used to realize the autonomous multistable 4D Yu–Wang chaotic system on FPGA, so that it can be applied in embedded engineering based on chaos. Experiments show that the maximum operating frequency of the Yu–Wang chaotic oscillator designed based on FPGA is 161.212 MHz.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
    Published by Hindawi
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  • 2
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    Calibration of the Volatility in Option Pricing Using the Total Variation Regularization (2014)
    Hindawi
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    Publication Date: 2014-03-26
    Description: In market transactions, volatility, which is a very important risk measurement in financial economics, has significantly intimate connection with the future risk of the underlying assets. Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation regularization strategy, a bivariate total variation regularization model is proposed to estimate the implied volatility. We not only prove the existence of the solution, but also provide the necessary condition of the optimal control problem—Euler-Lagrange equation. The stability and convergence analyses for the proposed approach are also given. Finally, numerical experiments have been carried out to show the effectiveness of the method.
    Print ISSN: 1110-757X
    Electronic ISSN: 1687-0042
    Topics: Mathematics
    Published by Hindawi
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  • 3
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    The Adjoint Method for the Inverse Problem of Option Pricing (2014)
    Hindawi
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    Publication Date: 2014-03-27
    Description: The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS) to find the optimal and numerical examples shows the effectiveness of the presented method.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
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  • 4
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    A Line-Search-Based Partial Proximal Alternating Directions Method for Separable Convex Optimization (2014)
    Hindawi
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    Publication Date: 2014-05-08
    Description: We propose an appealing line-search-based partial proximal alternating directions (LSPPAD) method for solving a class of separable convex optimization problems. These problems under consideration are common in practice. The proposed method solves two subproblems at each iteration: one is solved by a proximal point method, while the proximal term is absent from the other. Both subproblems admit inexact solutions. A line search technique is used to guarantee the convergence. The convergence of the LSPPAD method is established under some suitable conditions. The advantage of the proposed method is that it provides the tractability of the subproblem in which the proximal term is absent. Numerical tests show that the LSPPAD method has better performance compared with the existing alternating projection based prediction-correction (APBPC) method if both are employed to solve the described problem.
    Print ISSN: 1110-757X
    Electronic ISSN: 1687-0042
    Topics: Mathematics
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  • 5
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    Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales (2014)
    Hindawi
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    Publication Date: 2014-02-10
    Description: A class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale or . Moreover, we present illustrative numerical examples to show the feasibility of our results.
    Print ISSN: 1110-757X
    Electronic ISSN: 1687-0042
    Topics: Mathematics
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  • 6
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    Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors (2020)
    Hindawi
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    Publication Date: 2020-05-19
    Description: In this work, a novel 6D four-wing hyperchaotic system with a line equilibrium based on a flux-controlled memristor model is proposed. The novel system is inspired from an existing 5D four-wing hyperchaotic system introduced by Zarei (2015). Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. When a suitable set of parameters are chosen, the system exhibits a rich repertoire of dynamic behaviors including double-period bifurcation of the quasiperiod, a single two-wing, and four-wing chaotic attractors. Further analysis of the novel system shows that the multiple coexisting attractors can be observed with different system parameter values and initial values. Moreover, the feasibility of the proposed mathematical model is also presented by using Multisim simulations based on an electronic analog of the model. Finally, the active control method is used to design the appropriate controller to realize the synchronization between the proposed 6D memristive hyperchaotic system and the 6D hyperchaotic Yang system with different structures. The Routh–Hurwitz criterion is used to prove the rationality of the controller, and the feasibility and effectiveness of the proposed synchronization method are proved by numerical simulations.
    Print ISSN: 1076-2787
    Electronic ISSN: 1099-0526
    Topics: Computer Science , Mathematics
    Published by Hindawi
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  • 7
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    Stability Control of Staged Filling Construction on Soft Subsoil Using Hyperbolic Settlement Prediction Method: A Case Study of a Tidal Flat in China (2020)
    Hindawi
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    Publication Date: 2020-08-08
    Description: An improved method, which combines in situ measured settlement data, hyperbolic method, and deep lateral displacement rate, is presented in this study to predict the consolidation and stability of the ground, which can be used in conducting staged filling construction on soft subsoil. A case history of a highway embankment construction in a tidal flat with thick mucky clay is studied in Xia Pu, China. Preloading with the prefabricated vertical drain method is adopted to accelerate the consolidation of a subgrade. The field behavior of soft ground under filling load is observed through in situ monitoring sensors in four typical sections. The final ground settlement in each stage is determined using the field monitoring data based on the hyperbolic settlement prediction method. For each stage of graded filling load, the ground settlement with a strain consolidation degree of 95% is defined as the standard settlement, and the corresponding settlement time is set as the standard settlement time. The preloading period is estimated according to the standard settlement time. The deep lateral displacement rate of the ground is monitored to control the stability of the foundation and recommended to guide the embankment construction. Results indicate that the presented method can predict the preloading time of graded filling, reduce the frequency of observation, and ensure the consolidation and stability of the ground.
    Print ISSN: 1687-8086
    Electronic ISSN: 1687-8094
    Topics: Architecture, Civil Engineering, Surveying
    Published by Hindawi
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  • 8
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    CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua’s Chaotic System with Coexisting Multiple Attractors (2020)
    Hindawi
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    Publication Date: 2020-03-21
    Description: In this paper, a multistable modified fourth-order autonomous Chua’s chaotic system is investigated. In addition to the dynamic characteristics of the third-order Chua’s chaotic system itself, what interests us is that this modified fourth-order autonomous Chua’s chaotic system has five different types of coexisting attractors: double-scroll, single band chaotic attractor, period-4 limit cycle, period-2 limit cycle, and period-1 limit cycle. Then, an inductorless modified fourth-order autonomous Chua’s chaotic circuit is proposed. The active elements as well as the synthetic inductor employed in this circuit are designed using second-generation current conveyors (CCIIs). The reason for using CCIIs is that they have high conversion rate and operation speed, which enable the circuit to work at a higher frequency range. The Multisim simulations confirm the theoretical estimates of the performance of the proposed circuit. Finally, using RK-4 numerical algorithm of VHDL 32-bit IQ-Math floating-point number format, the inductorless modified fourth-order autonomous Chua’s chaotic system is implemented on FPGA for the development of embedded engineering applications based on chaos. The system is simulated and synthesized on Virtex-6 FPGA chip. The maximum operating frequency of modified Chua’s chaotic oscillator based on FPGA is 180.180 MHz. This study demonstrates that the hardware-based multistable modified fourth-order autonomous Chua’s chaotic system is a very good source of entropy and can be applied to various embedded systems based on chaos, including secure communication, cryptography, and random number generator.
    Print ISSN: 1076-2787
    Electronic ISSN: 1099-0526
    Topics: Computer Science , Mathematics
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  • 9
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    Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors (2020)
    Hindawi
    Details
    Publication Date: 2020-03-30
    Description: Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.
    Print ISSN: 1076-2787
    Electronic ISSN: 1099-0526
    Topics: Computer Science , Mathematics
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  • 10
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    Cooperative Solution of Multi-UAV Rendezvous Problem with Network Restrictions (2015)
    Hindawi
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    Publication Date: 2015-01-01
    Description: By considering the complex networks, the cooperative game based optimal consensus (CGOC) algorithm is proposed to solve the multi-UAV rendezvous problem in the mission area. Firstly, the mathematical description of the rendezvous problem is established, and the solving framework is provided based on the coordination variables and coordination function. It can decrease the transmission of the redundant information and reduce the influence of the limited network on the task. Secondly, the CGOC algorithm is presented for the UAVs in distributed cooperative manner, which can minimize the overall cost of the multi-UAV system. The CGOC control problem and the corresponding solving protocol are given by using the cooperative game theory and sensitivity parameter method. Then, the CGOC method of multi-UAV rendezvous problem is proposed, which focuses on the trajectory control of the platform rather than the path planning. Simulation results are given to demonstrate the effectiveness of the proposed CGOC method under complex network conditions and the benefit on the overall optimality and dynamic response.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
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