Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections, Rates and Inputs

Download

index.pdf

Date

2022-11-01

Author

Akhmet, Marat
Tleubergenova, Madina
Zhamanshin, Akylbek

Metadata

Show full item record

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

Item Usage Stats

167
views

81
downloads

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.

Subject Keywords

Hopfield-type neural networks, modulo periodic unpredictable synaptic connections, rates and inputs, unpredictable solutions, exponential stability, numerical simulations, EXPONENTIAL STABILITY, GRADED RESPONSE, POINCARE CHAOS, EXISTENCE, SEGMENTATION, OSCILLATION

URI

https://hdl.handle.net/11511/101804

Journal

ENTROPY

DOI

https://doi.org/10.3390/e24111555

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2022-06-01) Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Poisson stable components. The first component guarantees the Poisson stability of the dynamics, and the second one causes irregular oscillations. The inputs are Poisson stable to take into account the more sophisticated environment of the networks. The rates and inputs are synchronized to obt...
Global exponential stability of neural networks with non-smooth and impact activations Akhmet, Marat (2012-10-01) In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
State-dependent impulsive Cohen-Grossberg neural networks with time-varying delays Sayli, Mustafa; YILMAZ, ENES (2016-01-01) In this paper, a more general class of state-dependent impulsive Cohen-Grossberg neural networks having variable coefficients with time-varying delays is addressed. By means of B-equivalence method, we reduce this state-dependent impulsive neural networks system to a fix time impulsive neural networks system. Sufficient conditions for existence and global exponential stability of the equilibrium point as well as periodic solution are obtained by employing a suitable Lyapunov function, the Banach fixed point...
Periodic solution for state-dependent impulsive shunting inhibitory CNNs with time-varying delays Sayli, Mustafa; YILMAZ, ENES (2015-08-01) In this paper, we consider existence and global exponential stability of periodic solution for state-dependent impulsive shunting inhibitory cellular neural networks with time-varying delays. By means of B-equivalence method, we reduce these state-dependent impulsive neural networks system to an equivalent fix time impulsive neural networks system. Further, by using Mawhin's continuation theorem of coincide degree theory and employing a suitable Lyapunov function some new sufficient conditions for existence...
Stability in cellular neural networks with a piecewise constant argument Akhmet, Marat; Yılmaz, Elanur (2010-03-01) In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.

Citation Formats

M. Akhmet, M. Tleubergenova, and A. Zhamanshin, “Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections, Rates and Inputs,” ENTROPY, vol. 24, no. 11, pp. 0–0, 2022, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/101804.