Chaotification of Impulsive Systems by Perturbations

Fen, Mehmet Onur
Akhmet, Marat
In this paper, we present a new method for chaos generation in nonautonomous impulsive systems. We prove the presence of chaos in the sense of Li-Yorke by implementing chaotic perturbations. An impulsive Duffing oscillator is used to show the effectiveness of our technique, and simulations that support the theoretical results are depicted. Moreover, a procedure to stabilize the unstable periodic solutions is proposed.


Chaos generation in hyperbolic systems
Akhmet, Marat; FEN, MEHMET ONUR (2012-01-01)
© 2012 L & H Scientific Publishing, LLC.In the present paper, we consider extension of chaos in hyperbolic systems with arbitrary large dimensions. Our investigations comprise chaos in the sense of both Devaney and Li-Yorke. We provide a mechanism for unidirectionally coupled systems through the insertion of chaos from one system to another, where the latter is initially nonchaotic. In our procedure for the chaos extension, we take advantage of chaotic sets of functions to provide mathematically approved re...
Fen, Mehmet Onur; Akhmet, Marat (2016-06-01)
In the present study, we investigate the dynamics of shunting inhibitory cellular neural networks (SICNNs) with impulsive effects. We give a mathematical description of the chaos for the multidimensional dynamics of impulsive SICNNs, and prove its existence rigorously by taking advantage of the external inputs. The Li-Yorke definition of chaos is used in our theoretical discussions. In the considered model, the impacts satisfy the cell and shunting principles. This enriches the applications of SICNNs and ma...
Tikhonov theorem for differential equations with singular impulses
Akhmet, Marat (2018-01-01)
The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is applied to proof the main theorems. Illustrative examples with simulations are given to support the theoretical results.
Stochastic inventory modelling t
Özkan, Erhun; Serin, Yaşar Yasemin; Department of Industrial Engineering (2010)
In this master thesis study, new inventory control mechanisms are developed for the repairables in Nedtrain. There is a multi-item, multi echelon system with a continuous review and one for one replenishment policy and there are different demand supply options in each control mechanism. There is an aggregate mean waiting time constraint in each local warehouse and the objective is to minimize the total system cost. The base stock levels in each warehouse are determined with an approximation method. Then dif...
Almost Periodic Solutions of Recurrent Neural Networks with State-Dependent and Structured Impulses
Akhmet, Marat; Erim, Gülbahar (2023-01-01)
The subject of the present paper is recurrent neural networks with variable impulsive moments. The impact activation functions are specified such that the structure for the jump equations are in full accordance with that one for the differential equation. The system studied in this paper covers the works done before, not only because the impacts have recurrent form, but also impulses are not state-dependent. The conditions for existence and uniqueness of asymptotically stable discontinuous almost periodic s...
Citation Formats
M. O. Fen and M. Akhmet, “Chaotification of Impulsive Systems by Perturbations,” INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, pp. 0–0, 2014, Accessed: 00, 2020. [Online]. Available: