Nonlinear Dynamics

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Stability Switches and Double Hopf Bifurcation Analysis on Two-Degree-of-Freedom Coupled Delay van der Pol Oscillator

Yani Chen et al.

Summary: This paper examines the influence of two-degree-of-freedom coupled van der Pol oscillators with time delay feedback using normal form and central manifold theories. The results show the relationship between system stability and time delay, as well as the complexity of its dynamical behavior. Practical engineering problems can utilize time delay feedback adjustment to achieve effects such as amplitude death and limit loop based on the characteristics of the system.

MATHEMATICS (2021)

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New Irregular Solutions in the Spatially Distributed Fermi-Pasta-Ulam Problem

Sergey Kashchenko et al.

Summary: This paper explores irregular solutions of the spatially-distributed Fermi-Pasta-Ulam (FPU) equation, constructing families of special nonlinear systems known as Schrodinger type-quasinormal forms. These systems determine the local behavior of solutions to the original problem as t approaches infinity. The paper also discusses the asymptotics of the main solution of the FPU equation and the interaction of waves moving in opposite directions, as well as the complications arising from perturbing the number of elements in a chain.

MATHEMATICS (2021)

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LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation

Hamede Karami et al.

Summary: In this study, an observer-based state feedback stabilizer design for a class of chaotic systems in the presence of external perturbations and Lipchitz nonlinearities is presented. The linear matrix inequality method is utilized to design a state feedback controller, ensuring asymptotical stability based on Lyapunov theorem. The stability of the closed-loop system is achieved by minimizing the effects of nonlinear perturbations and disturbances through optimizing stabilizer and observer parameters.

MATHEMATICS (2021)

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Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

Wahyudin Nur et al.

Summary: This paper discusses a schistosomiasis model with a snail predator as a biological control agent, proving that the solutions are non-negative and bounded, investigating the existence condition of equilibrium points, and determining the basic reproduction number. Various stability conditions, including local and global stability, are proved using different criteria. Numerical simulation results support the effectiveness of using a snail predator to control schistosomiasis spread.

MATHEMATICS (2021)

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On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities

Alexander N. Pchelintsev

Summary: This article discusses the search procedure for Poincare recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system, using a previously developed high-precision numerical method. The Lyapunov exponents are calculated for the resulting limiting solution, using the modified Benettin's algorithm to study the stability of the found regime and confirm the type of attractor.

MATHEMATICS (2021)

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