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  • Biological Neural Network& Nonlinear Dynamics Biological Neural NetworkSimilar Neural Network to Real Neural Networks Membrane PotentialPotential of within Cell to outside Potential of Cell

  • Hodgkin-Huxley ModeltHyperpolarization state(Resting State): Before Stimulate(Depolarization): After StimulateV, m, n, h: State variables 4-D Phase SpaceIon gate consider role, Real Firing(O) (V: Membrane Potential, m: Na+ Activation Gaten: K+ Activation Gate, h: Na+ Inactivation Gate)(Recovery) h , n , Hyperpolarization State Resting State(Repolarization)Action Potential Mechanism m , h: Open State, Na+: OutIn h0(Approach), n , K+: InOut

  • Integrate-and-Fire ModelIon Gate Ignores Role, Firing Assumed Resting StateConsidering Firing by only External Stimulus* Temporal Integrator Function: Time constant (Large enough) Leakage ignore In case of (Input Stimulus) > Threshold Keep firing* Coincident Detector Function: Time constant (Small enough), Leakage(Large enough) Most of time: resting state, At same Time Multiple input Stimulus > Threshold Firing StateSimplified Model McCulloch Model, PerceptronIgnore Dynamic Characteristic of NeuronCompare only Stimulus Intensity and Threshold Check Firing

  • Phase Space Analysis of Morris-Lecar model* Morris-Lecar ModelIon gate consider role, Real Firing(O)V, w: State variables 2-D Phase Space(V: Membrane Potential, w: Recovery variable)Vw* Nullclines: Change Rate of State Variables Ex) V-nullclines: dV/dt=0, w-nullclines: dw/dt=0for Change of Time = 0Threshold* 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 ofWeak ExternalStimulusFiring according toFrequency of WeakExternal StimulusFrequencyof NoiseResonance Coupling of Neurons Electrical Coupling, Chemical Coupling(Coupling of Neurons in Brain: Most Chemical Coupling)* Reaction Velocity Chemical Coupling

    Chemical Coupling

  • Coupling of Neurons* Synchronization and Anti-synchronization by CombiningSynchronization: At Same Time FiringAnti-synchronization: At Different Times FiringSynchronization & Anti-synchronization by Chemical CouplingSynchronizationBy ExcitatoryCouplingReversalPotential>RestingPotentialHow?Anti-SynchronizationBy InhebitoryCouplingReversalPotential
  • Coupling Nervous System* Central Pattern Generator(CPG), Visual Nervous System Models+Dynamic Characteristicof NeuronCouplingbetween NeuronsResult from Dynamic Characteristic of Neural NetworkBrain Wave Analysis, etc.Recent Researched Nervous System and Research Trends(CPG: Biorhythm Control Nervous System)