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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 48584 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Razvan, Mohammad Reza
- Abstract:
- This thesis presents an investigation of the dynamics of two coupled non-identical FitzHugh–Nagumo neurons. It is known that signal transmission in coupled neurons is not instantaneous in general, and time delay is inevitable in signal transmission for real neurons. Therefore we consider the system of two coupled neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich and we will study the excitability of the neurons. By bifurcation study of the system the coupling strength and delay-dependent stability regions are illustrated in the parameter plane, to describe typical behaviors, such as synchronized and anti-phase periodic solutions, or coexistence of these states, quiescence, and also multi-stability. Also we will describe the differences between delayed and instantaneous systems. We try to describe the impact of stated parameters in appearance or disappearance of synchronized solutions and the mechanisms for transition from synchronized to anti-phase solutions or vice versa. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behaviors are clarified. Actually this kind of bifurcation study is a serious task for the prediction and detection of all possible dynamical behaviors. Missing some kind of solutions is possible, if we only aid simulation study
- Keywords:
- Delay ; Stability ; Neuron ; Bifurcation ; Synchronization Control ; Multiple Equilibria ; Neuronal Models
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