IRJMST Vol 7 Issue 12 [Year 2016] ISSN 2250 – 1959 (0nline) 2348 – 9367 (Print) International Research Journal of Management Science & Technology http://www.irjmst.com Page 325 Stability analysis of discrete time neural networks with leakage delay and discrete delay S. Nalini 1 *, Dr. S. Mehar Banu 2 1 Research Scholar, Bharathiyar University, Research and Development centre, Coimbatore, Tamilnadu. India,E-mail ID: nalininsit@gmail.com 2 Assistant Professor, Department of Mathematics,Govt. Arts college for women, Salem – 636 008,Tamilnadu, India,E –mail ID: meharizh@gmail.com Abstract : This paper is concerned with a discrete time neural neural networks with leakage delay and discrete delay. Based on a discrete halanay type inequality, a new global stability condition for nonlinear difference equation is derived. In testing purpose two neurons were used. The impulse response is done by matlab to analyze the stability of the system. 1. Introduction: Recently the study of dynamical neural networks has concerned researchers because of its extensive applications in mixture of areas such as image processing, Signal processing, parallel computation, pattern recognition, associative memory, control engineering and so on. Practically discrete time systems have been used for variety of fields such as electrical network, ultrasonic, quantum waves, genetics, computer vision etc,. And these applications are generally depends on stability of the neural networks and it is well known that delays are frequently the sources of instability and oscillation in system. Therefore the stability analysis of discrete time neural networks with delays becomes an important topic of theoretical studies in neural networks.. In [2] - [4], [7]-[9], [12] the continuous time delays were investigated based on matrix measure , Lyapunov functional , linear matrix inequality and fixed point theory. Compared with the continuous time delays very less consideration has been paid to discrete time delay neural networks [1], [6], [10], [11], [13]. In [11] & [13] authors considered discrete time delay system and investigated global exponential stability by using a discrete time version of Halanay inequality. From the motivation of the above literature, in this paper we will consider the problem of global exponential stability of discrete time neural networks with leakage and discrete delays. Moreover new discrete Halanay type inequality was derived. The structure of this paper was arranged as follows in section 2; we have introduced discrete time neural works with time delays and presented some preliminaries which will be used throughout this paper. In section3, we have derived new discrete Halanay type inequality. In section4, Global exponential stability criteria are derived by using new discrete type inequality. Finally numerical examples are given to illustrate the effectiveness of our proposed method.