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 Model
t
Hyperpolarization state
Ⅰ Ⅱ Ⅲ Ⅳ
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 Gaten: 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 ModelIon 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=0for Change of Time = 0 Threshol
d
Ⅰ Ⅱ
* 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
ExternalStimulus
⇒
Firing according to
Frequency of Weak
External Stimulus
Frequencyof Noise
Resonance
• Coupling of Neurons→ Electrical Coupling, Chemical Coupling
(Coupling of Neurons in Brain: Most Chemical Coupling)
* Reaction Velocity
Chemical
Coupling< Chemica
l Coupling
* Diversity of Reaction
Chemical
Coupling> Chemica
l 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 ExcitatoryCoupling
Reversal
Potential
>RestingPotenti
al
How?
⇒Anti-Synchronization → By Inhebitory
Coupling
Reversal
Potential
<RestingPotenti
al
How?
⇒ Limited in weak interaction
• Coupling Nervous System
* Central Pattern Generator(CPG), Visual Nervous System Models
+Dynamic
Characteristicof Neuron
Couplingbetween Neurons
⇒Result from
Dynamic Characteristic of Neural Network
Brain Wave Analysis, etc.
Recent Researched Nervous System and Research Trends
(CPG: Biorhythm Control Nervous System)