Domain-Structured Chaos in a Hopfield Neural Network

Date

2019-12-30

Author

Akhmet, Marat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

263
views

0
downloads

In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic regime, the formed set is invariant under the system governing the dynamics of the neural network. The approach can be viewed as an extension of the unimodality technique for one-dimensional map, thereby generating chaos from higher-dimensional systems. We show that the discrete Hopfield neural network considered is chaotic in the sense of Devaney, Li-Yorke, and Poincare. Mathematical analysis and numerical simulation are provided to confirm the presence of chaos in the network.

Subject Keywords

Modelling and Simulation, Applied Mathematics

URI

https://hdl.handle.net/11511/57687

Journal

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

DOI

https://doi.org/10.1142/s0218127419502055

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Non-autonomous equations with unpredictable solutions Akhmet, Marat (Elsevier BV, 2018-06-01) To make research of chaos more amenable to investigating differential and discrete equations, we introduce the concepts of an unpredictable function and sequence. The topology of uniform convergence on compact sets is applied to define unpredictable functions [1,2]. The unpredictable sequence is defined as a specific unpredictable function on the set of integers. The definitions are convenient to be verified as solutions of differential and discrete equations. The topology is metrizable and easy for applica...
Shunting inhibitory cellular neural networks with strongly unpredictable oscillations Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (Elsevier BV, 2020-10-01) The paper considers a new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations. The conditions for the existence, uniqueness and stability of the solutions are determined. Numerical examples are given to show the feasibility of the obtained results.
Global existence and boundedness for a class of second-order nonlinear differential equations Tiryaki, Aydin; Zafer, Ağacık (Elsevier BV, 2013-09-01) In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form
LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM Dosi, Anar (American Mathematical Society (AMS), 2011-02-01) In the present paper we introduce quantum measures as a concept of quantum functional analysis and develop the fractional space technique in the quantum (or local operator) space framework. We prove that each local operator algebra (or quantum *-algebra) has a fractional space realization. This approach allows us to formulate and prove a noncommutative Albrecht-Vasilescu extension theorem, which in turn solves the quantum moment problem.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01) In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.

Citation Formats

M. Akhmet, “Domain-Structured Chaos in a Hopfield Neural Network,” INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, pp. 0–0, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57687.