Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to...

7
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

Transcript of Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to...

Page 1: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

Biological Neural Network& Nonlinear Dynamics

• Biological Neural NetworkSimilar Neural Network to Real Neural Networks

• Membrane PotentialPotential of within Cell to outside Potential of Cell

Page 2: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

• 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

Page 3: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

• 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

Page 4: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

• 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

Page 5: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

• 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

Page 6: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

• 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

Page 7: Biological Neural Network & Nonlinear Dynamics Biological Neural Network Similar Neural Network to Real Neural Networks Membrane Potential Potential of.

• 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)