Informatics Publishing Limited

G. Padmavathi ¹, Shahnaz Bathul ¹, P. V. Siva Kumar ²

Affiliations
1 Department of Mathematics, JNTU Hyderabad, IN
2 Department of Computer Science, VNRVJIET, Hyderabad, IN

Abstract

In this paper continuous hysteretic neuron model has been studied and discretized the model by using proper approximation. Sufficient condition for global exponential stability of a unique equilibrium is obtained. Motivated by the applications of bidirectional associative neural networks with hysteresis in artificial neural networks, we studied the global dynamics of bidirectional associative neural network with hysteresis. The hysteretic neural network model is envisaged to be efficient and robust for various applications such as medical image processing, military data processing, etc. Hysteretic feedback control phenomena also manage glucose vs. lactose utilization preference in Escherichia coli and ensure unidirectional cell-cycle progression in eukaryotes. The result improves the earlier publications due to the bidirectional associative memory and it removes restrictions on the neutral delays. Our result shows that after discretization of hysteretic neuron models, the network converges to a stable state and this result has been applied through numerical example. The outcomes are explicit in the sense that the criteria obtained are easily verifiable as they are expressed in terms of the parameters of the system.

Keywords

Descretization, Hysteretic Neural Network, Bidirectional Associative, Global Exponential Stability.

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T. Vidyanath ¹, K. Lakshmi Narayana ², Shahnaz Bathul ³

Affiliations
1 Dept. of Mathematics, AVNIET, Hyderabad, IN
2 Dept. of Mathematics, VITS, Hyderabad, IN
3 Dept. of Mathematics, JNTUH, Hyderabad, IN

Abstract

In this paper, we study a three species eco-system with a predator and two preys. Employing suitable techniques like Routh-Hurwitz criterion and Lyapunov, the local and global stability at the interior equilibrium point is analyzed. Also using Weiner process, the stochastic model corresponding to the deterministic model is constructed and it’s exponential and mean square stability at the trivial solution is derived. Finally numerical simulations authenticate the existence of the system.

Keywords

Prey-Predation, Routh-Hurwitz Criterion, Global Stability, Stochastic Process.

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