Swati Tyagi

Stability Analysis of an Integro Differential Equation Model of Ring Neural Network with Delay

In this paper we present and study a ring neural network model with delays. We study existence and uniqueness of equilibrium point and global stability of the model system. At the end few examples have been given to illustrate the analytical findings.

Stability and synchronization of delayed fractional-order projection neural network with piecewise constant argument of mixed type

Abstract Projection equations arise in several optimization problems and possess significant applications in many areas of science and engineering. In this paper, we propose a fractional-order projection neural network to solve quadratic programming problems. We study stability and synchronization for a class of delayed projection neural networks of mixed type via impulsive control. Using concepts of fractional calculus, we investigate the existence of solution and study its global asymptotic stability. Moreover, we propose an effective impulsive control scheme to achieve synchronization for the system. We demonstrate the validity and transient behaviour of the proposed neural network with the help of suitable examples.

Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals

Abstract In this paper, we study convergence characteristics of a class of continuous time fractional-order cellular neural network containing delay. Using the method of Lyapunov and Mittag-Leffler functions, we derive sufficient condition for global Mittag-Leffler stability, which further implies global asymptotic stability of the system equilibrium. Based on the theory of fractional calculus and the generalized Gronwall inequality, we approximate the solution of the corresponding neural network model using discretization method by piecewise constant argument and obtain some easily verifiable conditions, which ensures that the discrete-time analogues preserve the convergence dynamics of the continuous-time networks. In the end, we give appropriate examples to validate the proposed results, illustrating advantages of the discrete-time analogue over continuous-time neural network for numerical simulation.

Global asymptotic and exponential synchronization of ring neural network with reaction–diffusion term and unbounded delay

In this paper, we consider a ring neural network of coupled neurons with distributed and discrete time-varying delays along with the reaction–diffusion terms. We derive sufficient conditions that ensure the existence and uniqueness of the equilibrium point, synchronized asymptotic stability and exponential synchronization by using the theory of topological degree, properties of M-matrix, Lyapunov functional and analytic methods. The obtained results remove the assumption on the boundedness of activation functions. At the end, we give two examples to show the validity of our analysis.

Global dynamics and parameter identifiability in a predator-prey interaction model

Abstract This paper discusses a predator-prey model with prey refuge. We investigate the role of prey refuge on the existence and stability of the positive equilibrium. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional, which shows that the prey refuge has no influence on the permanence property of the system. Mathematically, we analyze the effect of increase or decrease of prey reserve on the equilibrium states of prey and predator species. To access the usability of proposed predator-prey model in practical scenarios, we also suggest, the use of Levenberg-Marquardt (LM) method for associated parameter estimation problem. Numerical results demonstrate faithful reconstruction of system dynamics by estimated parameter by LM method. The analytical results found in this paper are illustrated with the help of suitable numerical examples