Fatma Tokmak Fen

SICNNs with Li-Yorke chaotic outputs on a time scale

The existence of Li-Yorke chaos in the dynamics of shunting inhibitory cellular neural networks (SICNNs) on time scales is investigated. It is rigorously proved by taking advantage of external inputs that the outputs of SICNNs exhibit Li-Yorke chaos. The theoretical results are supported by simulations, and the controllability of chaos on the time scale is demonstrated by means of the Pyragas control technique. This is the first time in the literature that the existence as well as the control of chaos are provided for neural networks on time scales. HighlightsChaotic dynamics of SICNNs on time scales is considered.The results are based on the Li-Yorke definition of chaos.Controllability of the chaos on time scales is numerically demonstrated.Simulations which support the theoretical results are depicted.This is the first paper which considers chaos for neural networks on time scales.

Positive Solutions of nth-Order Boundary Value Problems with Integral Boundary Conditions

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

Homoclinic and heteroclinic motions in hybrid systems with impacts

In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the systems are under the influence of a discrete map that possesses homoclinic and heteroclinic orbits. Simulations that support the theoretical results are represented by means of a Duffing equation with impacts. c ©2017 Mathematical Institute Slovak Academy of Sciences

Positive solutions of nth-order m-point impulsive boundary value problems

Abstract This paper is concerned with the existence of positive solutions of an nth-order m-point impulsive boundary value problem. Existence results of at least three positive solutions are established via a fixed point theorem in a cone due to Avery–Peterson. Also, an example is given to illustrate the effectiveness of our result.

Homoclinical Structure of Retarded SICNNs with Rectangular Input Currents

The dynamics of retarded shunting inhibitory cellular neural networks (SICNNs) with rectangular input currents is investigated from the asymptotic point of view. It is rigorously proved that such networks possess homoclinic and heteroclinic outputs under certain conditions. Illustrative examples that support the theoretical results are provided. Moreover, the extension of the homoclinical structure is numerically demonstrated for unidirectionally coupled retarded SICNNs.

Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem

Abstract In this paper, six functionals fixed point theorem is used to investigate the existence of at least three positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem. As an application, we give an example to demonstrate our result.

Positive solutions of boundary value problems for

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with

p

p

-Laplacian fractional differential equations

-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

Positive solutions of nth-order impulsive differential equations with integral boundary conditions

Abstract This paper is concerned with the existence and nonexistence of positive solutions of nth-order impulsive boundary value problem with integral boundary conditions. The fixed point theorem of cone expansion and compression is used to investigate the existence of at least one positive solution. Also, an example is given to illustrate the effective of our results.