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Abstract
This paper deals with the synchronisation problem for an array of coupled complex discrete-time networks with the presence of randomly occurring information. The time-varying delays, parameter uncertainties and nonlinearities enter into the system in a random way and such randomly occurring time-delays, randomly occurring uncertainties and randomly occurring sector-like nonlinearities obey certain mutually uncorrelated Bernoulli-distributed white-noise sequences. By employing direct delay decomposition approach and constructing suitable Lyapunov–Krasovskii functional, sufficient conditions are established to ensure the synchronisation criteria for the complex networks with randomly occurring information in terms of linear matrix inequalities. Finally, in numerical examples, synchronisation of Barabàsi Albert scale-free networks and chaotic synchronisation of Lorenz system are rendered to exemplify the effectiveness and applicability of the proposed results.
Acknowledgements
The authors are grateful to the editor, associate editor and anonymous reviewers for their insightful comments and constructive suggestions to improve the quality of the manuscript.
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L. Jarina Banu
L. Jarina Banu graduated and postgraduated in Mathematics from Gandhigram Rural Institute – Deemed University, Tamil Nadu, India, in 2008 and 2011, respectively. Currently, under Maulana Azad National Fellowship of University Grants Commission, Government of India, New Delhi, she is pursuing PhD degree under the supervision of Prof. P. Balasubramaniam in the Department of Mathematics, Gandhigram Rural Institute – Deemed University, India. Her research interest is in the area of stability analysis of discrete dynamical systems including switched systems, fuzzy systems and complex networks.
P. Balasubramaniam
P. Balasubramaniam postgraduated from the Department of Mathematics of Gobi Arts College affiliated to Bharathiar University, Coimbatore, in the year 1989. He was awarded Master of Philosophy in the year 1990 and Doctor of Philosophy (PhD) in 1994 in the field of Mathematics with specialised area of Control Theory from the Department of Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, India. Soon after his completion of PhD degree, he served as lecturer in Mathematics in Engineering Colleges for 3 years. Since February 1997, he served as lecturer and subsequently reader in Mathematics for 5 years in the Gandhigram Rural University, Gandhigram, Tamil Nadu, India. He is rendering his services as a professor and head, Department of Mathematics, Gandhigram Rural University, Gandhigram, India, from November 2006 till date. He has worked as a visiting research professor during the years 2001 and 2005–2006 for promoting research in the field of control theory and neural networks at Pusan National University, Pusan, South Korea. Also, he has worked as visiting professor in the Institute of Mathematical Sciences, University of Malaya, Malaysia, for the period of 6 months from September 2011 to March 2012. He is a member of several academic bodies including a life member of Cryptology Research Society of India, Indian Statistical Institute, Kolkata, India. He has 23 years of experience in teaching and research. He has published more than 160 research papers in various SCI journals holding impact factors with Scopus H-index 19 and web of knowledge H-Index 12. Also, he has edited seven proceedings including a book and three international conference proceedings in Springer publications. He has published research articles in national journals and international conference proceedings. He is serving as a reviewer of many SCI journals and member of the editorial board of Journal of Computer Science and Advances in Fuzzy Sets and Systems. He is an editor-in-chief of the journal Modern Instrumentation, ISSN 2165-9257 and associate editor of College Sadhana – Journal for Bloomers of Research. He has received the Tamil Nadu Scientist Award (TANSA) for the discipline of Mathematical Sciences instituted by the Tamil Nadu State Council for Science and Technology in the year 2005. His research interest includes the areas of control theory, stochastic differential equations, soft computing, stability analysis, cryptography, neural networks, image processing and reaction–diffusion equations.