Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

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Presentation transcript:

Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of within Cell to outside Potential of Cell

Hodgkin-Huxley Model t Hyperpolarization state ⅠⅡⅢⅣ Ⅰ (Resting State): Before Stimulate Ⅱ (Depolarization): After Stimulate V, m, n, h: State variables ⇒ 4-D Phase Space Ion gate consider role, Real Firing(O) (V: Membrane Potential, m: Na + Activation Gate n: K + Activation Gate, h: Na + Inactivation Gate) Ⅳ (Recovery) ⇒ h ↑, n ↓, Hyperpolarization State → Resting State Ⅲ (Repolarization) Action Potential Mechanism ⇒ m ↑, h: Open State, Na + : Out→In ⇒ h→0(Approach), n ↑, K + : In→Out

Integrate-and-Fire Model Ion Gate Ignores Role, Firing Assumed → Resting State Considering Firing by only External Stimulus * Temporal Integrator Function : Time constant τ(Large enough) → Leakage ignore ⇒ In case of ∑ (Input Stimulus) > Threshold → Keep firing * Coincident Detector Function : Time constant τ(Small enough), Leakage(Large enough) ⇒ Most of time: resting state, At same Time Multiple input Stimulus > Threshold → Firing State Simplified Model → McCulloch Model, Perceptron Ignore Dynamic Characteristic of Neuron Compare only Stimulus Intensity and Threshold → Check Firing

Phase Space Analysis of Morris-Lecar model * Morris-Lecar Model Ion gate consider role, Real Firing(O) V, w: State variables ⇒ 2-D Phase Space (V: Membrane Potential, w: Recovery variable) V w * Nullclines: Change Rate of State Variables Ex) V-nullclines: dV/dt=0, w-nullclines: dw/dt=0 for Change of Time = 0 Threshold ⅠⅡ * Bifurcation : Property of Attractor to Change According to External Stimulus * Bifurcation diagram : State Change of Neuron according to External Stimulus

Phase Space Analysis of Morris-Lecar model * Stochastic Resonance = Frequency of Weak External Stimulus ⇒ Firing according to Frequency of Weak External Stimulus Frequency of Noise Resonance Coupling of Neurons → Electrical Coupling, Chemical Coupling (Coupling of Neurons in Brain: Most Chemical Coupling) * Reaction Velocity Chemical Coupling < * Diversity of Reaction Chemical Coupling >

Coupling of Neurons * Synchronization and Anti-synchronization by Combining Synchronization: At Same Time Firing Anti-synchronization: At Different Times Firing Synchronization & Anti-synchronization by Chemical Coupling ⇒ Synchronization → By Excitatory Coupling Reversal Potential > Resting Potential How? ⇒ Anti-Synchronization → By Inhebitory Coupling Reversal Potential < Resting Potential How? ⇒ Limited in weak interaction

Coupling Nervous System * Central Pattern Generator(CPG), Visual Nervous System Models + Dynamic Characteristic of Neuron Coupling between Neurons ⇒ Result from Dynamic Characteristic of Neural Network Brain Wave Analysis, etc. Recent Researched Nervous System and Research Trends (CPG: Biorhythm Control Nervous System)