Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays |
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| Affiliation: | 1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;2. Hunan Women’s University, Changsha, Hunan 410002, PR China;1. College of Computer Science, Chongqing University, Chongqing 400044, China;2. College of Software Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;1. Complex Sciences Center, Shanxi University, Taiyuan 030006, PR China;2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, PR China;3. Ecological Complexity and Modeling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside, CA 92521-0124, USA;4. Department of Biology, University of California, Riverside, CA 92521, USA;1. College of Mathematics, Honghe University, Mengzi, Yunnan 661100, PR China;2. Department of Physics, Honghe University, Mengzi, Yunnan 661100, PR China;1. Department of Applied Mathematics, AGH University of Science and Technology, Krakow, Poland;2. Department of Mathematics, Hacettepe University, Ankara, Turkey |
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| Abstract: | In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations. |
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| Keywords: | Memristor Functional differential inclusions BAM neural networks Krasnoselskii’s fixed point theorem of set-valued maps Global dissipativity Positive periodic solution |
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