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Partial generalized synchronization theorems of differential and discrete systems

Jianyi Jing, Lequan Min, Geng Zhao (2008)

Kybernetika

This paper presents two theorems for designing controllers to achieve directional partial generalized synchronization (PGS) of two independent (chaotic) differential equation systems or two independent (chaotic) discrete systems. Two numerical simulation examples are given to illustrate the effectiveness of the proposed theorems. It can be expected that these theorems provide new tools for understanding and studying PGS phenomena and information encryption.

Passivity analysis of uncertain stochastic neural network with leakage and distributed delays under impulsive perturbations

Senthil Raj, Raja Ramachandran, Samidurai Rajendiran, Jinde Cao, Xiaodi Li (2018)

Kybernetika

In this paper, the problem of passivity analysis for a class of uncertain stochastic neural networks with mixed delays and impulsive control is investigated. The mixed delays include constant delay in the leakage term, discrete and distributed delays. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By using Lyapunov stability theory, stochastic analysis, linear matrix inequality...

Patchy Vector Fields and Asymptotic Stabilization

Fabio Ancona, Alberto Bressan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on ℝ n . We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin,...

Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

Zhen Wang, Wei Sun, Zhouchao Wei, Shanwen Zhang (2017)

Kybernetika

Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics at infinity...

Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces

Nguyen Thieu Huy, Ngo Quy Dang (2016)

Annales Polonici Mathematici

We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence, uniqueness...

Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.

Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.

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