Phase synchronization in two coupled chaotic neurons |
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| Institution: | 1. Department of Physics, University Institute of Sciences, Chandigarh University, Mohali 140413, India;2. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India;1. Physics Department, Federal University of Paraná, Curitiba, PR, Brazil;2. Physics Institute, University of São Paulo, São Paulo, SP, Brazil;3. Faculdade de Telêmaco Borba, FATEB, Telêmaco Borba, 84266-010, PR, Brazil;4. Graduate Program in Chemical Engineering Federal Technological University of Paraná, Ponta Grossa, Paraná, 84016-210, Brazil;5. Institute of Engineering, Science and Technology, Federal University of the Valleys of Jequitinhonha and Mucuri, Janaúba, MG, Brazil;6. Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, PR, Brazil;1. Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran, 159163-4311, Iran;2. Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran, 159163-4311, Iran |
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| Abstract: | Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rössler oscillators only having single time-scale mechanism. Using such a multiple time-scale model, the phase function can detect synchronization dynamics that cannot be distinguished by cross-correlation. Moreover, simulation results show that the Lyapunov exponents cannot be used as a definite criterion for the occurrence of chaotic phase synchronization for such a system. Evaluation of the phase function shows its utility in analyzing nonlinear neural systems. |
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