Nonautonomous Differential Systems Research Articles

On simple stability criteria for nonlinear neutral systems with multiple time delays

This work is concerned with the derivation of easily verifiable conditions for the asymptotic stability of a nonlinear nonautonomous neutral differential system. On introducing an adjusting function, the main results become less restrictive.

New existence results on periodic solutions of nonautonomous second order differential systems with $(q,p)$-Laplacian

New existence results on periodic solutions of nonautonomous second order differential systems with $(q,p)$-Laplacian

Stability of Hahnfeldt angiogenesis models with time lags

Mathematical models of angiogenesis, pioneered by Hahnfeldt, are under study. To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous delay differential systems with non-Lipschitz nonlinearities. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies.

Infinitely many periodic solutions for some second-order differential systems with p(t)-Laplacian

Abstract In this article, we investigate the existence of infinitely many periodic solutions for some nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained using critical point theory. 2000 Mathematics Subject Classification: 34C37; 58E05; 70H05.

Periodic solutions to second order nonautonomous differential systems with unbounded nonlinearities

We investigate the existence of periodic solutions of differential systems with a skew-symmetric matrix term and unbounded nonlinearities. Under new generalized Ahmad-Lazer-Paul conditions, some existence results are obtained and some results in the literature are improved.

PERIODIC SOLUTIONS OF SECOND-ORDER DIFFERENTIAL INCLUSIONS SYSTEMS WITH (q, p)-LAPLACIAN

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with (q, p)-Laplacian.

Periodic solutions to second order nonautonomous differential systems with gyroscopic forces

Existence of periodic solutions to second order differential systems with gyroscopic forces is considered via variational methods, where a generalized Ahmad–Lazer–Paul type condition is used. We do not impose the condition that the gyroscopic forces are small.

SOME EXISTENCE RESULTS ON PERIODIC SOLUTIONS OF ORDINARY (q, p)-LAPLACIAN SYSTEMS

Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian by the minimax methods in critical point theory.

Periodic solutions of a class of nonautonomous second order differential systems with $(q,p)$--Laplacian

Periodic solutions of a class of nonautonomous second order differential systems with $(q,p)$--Laplacian

Periodic Solutions for a Class of Nonautonomous Differential System with Impulses and Time-varying Delays

By employing Mawhin continuation theorem and constructing suitable Lyapunov functions, the existence and globally exponential stability of periodic solution for a class of nonautonomous differential system with impulses and time-varying delays are investigated in this paper. Some applications, an illustrative example and numerical simulations are given to show the effectiveness of the main results.

Preservation of exponential stability for linear non-autonomous functional differential systems

We consider preservation of exponential stability for a system of linear equations with a distributed delay under the addition of new terms and a delay perturbation. As particular cases, the system includes models with concentrated delays and systems of integrodifferential equations. Our method is based on Bohl–Perron type theorems.

Some existence results on periodic solutions of nonautonomous second-order differential systems with [formula omitted]-Laplacian

Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with ( q , p ) -Laplacian by using the least action principle and the minimax methods.

Global stability of a class of non-autonomous delay differential systems

This paper is concerned with a class of systems of non-autonomous delay differential equations which are defined on the non-negative function space. Under proper conditions, we employ a novel proof to establish several criteria of the global stability of a positive equilibrium. Moreover, we give two examples to illustrate our main results.

Minimum time control problems for non-autonomous differential equations

In this paper, we investigate a minimum time problem for controlled non-autonomous differential systems, with dynamics depending on the final time. The minimal time function associated to this problem does not satisfy the dynamic programming principle. However, we will prove that it is related to a standard front propagation problem via the reachability function. Two simple numerical examples are given to illustrate our approach.

Periodic solutions of nonautonomous differential systems modeling obesity population

In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.

Global exponential convergence and global convergence in finite time of non-autonomous discontinuous neural networks

The paper investigates global convergence of the solutions of a non-autonomous differential system with discontinuous right-hand side, arising from the description of the states of neurons in a general class of neural networks possessing discontinuous neuron activations in a time-varying situation. By exploring intrinsic features between the non-autonomous system and its asymptotic system, several novel sufficient conditions are derived which ensure global exponential convergence of the networks. Moreover, under some conditions, we prove that this networks possesses the property of global convergence in finite time, which cannot occur in smooth system. Our results can be easily verified and complement previous known criteria.

Some questions concerning attractors for non-autonomous dynamical systems

We compare various concepts of attractor in the context of non-autonomous dynamical systems. Then, we prove an appropriate version of the Pliss reduction principle for non-autonomous differential systems with rapidly oscillating coefficients.

A note on a nonlinear functional differential system with feedback control

In this note we apply Avery-Peterson multiple fixed point theorem to investigate the existence of multiple positive periodic solutions to the following non- linear non-autonomous functional differential system with feedback control ( dx dt = r(t)x(t) +F(t,xt,u(t �(t))), du dt = h(t)u(t) +g(t)x(t �(t)). We prove the system above admits at least three positive periodic solutions under certain growth conditions imposed on F.

Poincaré type theorems for non-autonomous systems

In this paper we establish analytic equivalence theorems of Poincaré and Poincaré–Dulac type for analytic non-autonomous differential systems based on the dichotomy spectrum of their linear part. As applications of the theorem, normal forms linearize for two illustrative examples.

The reflecting function and the small parameter method

The aim of this work is to combine the method of the reflecting function and the perturbation method to obtain sufficient conditions for the existence of a family of periodic solutions close to a given solution for multidimensional autonomous and non-autonomous differential systems.