Oscillatory properties of a differential inclusion of order and the asymptotic equivalence
Oscillatory properties of the fourth order linear differential equation
Oб инвариантности характеристических показателей линейных систем при экспоненциально убывающих возмущениях
Partial generalized synchronization theorems of differential and discrete systems
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
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
Patchy Vector Fields and Asymptotic Stabilization
This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on . 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
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 perturbations of non-conservative second order differential equations.
Periodic solutions for a numerical discretization neural network.
Periodic solutions of multispecies-competition predator-prey system with Holling's type III functional response and prey supplement.
Periodic solutions of the third order parametric differential equations involving large nonlinearities
Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces
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...
Periodicity and stability results for solutions of some fifth order nonlinear differential equations
Permanence and extinction of a generalized Gause-type predator-prey system with periodic coefficients.
Permanence of a discrete periodic Volterra model with mutual interference and Beddington-DeAngelis functional response.
Permanence of periodic predator-prey system with functional responses and stage structure for prey.
Permanence of periodic predator-prey system with general nonlinear functional response and stage structure for both predator and prey.
Permanence of predator-prey system with infinite delay.
Perron conditions and uniform exponential stability of linear skew-product semiflows on locally compact spaces.