Biological Neural Networks Nonlinear Dynamics Dynamic Characteristic of
Biological Neural Networks & Nonlinear Dynamics • Dynamic Characteristic of Nervous System Understanding of the interactions between neurons Neurons in a variety of nonlinear dynamical systems with dynamic characteristics Synchronized firing patterns of neurons in a group to express things Modeling biological nervous system as nonlinear dynamic for understanding structure of the nervous system. 1
• Neuron Models Composed of soma and axon and dendrite Dendrites receiving Signal processing in soma Convert to pulses in axon hillock Axons pass to other cells 1. Hodgkin Huxley Model Membrane potential changes due to external stimuli External stimuli Depolarization Ion leakage (K+) Ion influx (Na+) Potential decrease Potential increase hyper polarization Resting state Represent the action potential of nerve cells 2
2. Integrate and Fire Model Considering only fire the speech by an external stimulus Function according to the time constant τ when τ is large: Cumulative input stimulus. Fire threshold is greater than the input stimulus. ⇒ Temporal integrator when τ is small: Fire When Many inputs exceeds the threshold ⇒ Coincident detector Using Mc. Culloch-Pitts Model and Perceptron ⇒ Indicate whether the fire compared threshold with size of stimuli 3
• Analysis of Phase space Two-dimension model of neurons ◦ Morris-Lecar Model Indicate dynamic characteristics of neurons in two-dimensional phase space Indicate membrane potential by Ca+ ion and K+ ion 1. Zero line and firing line Intersection of V-zero line( resting state ) and w-zero line( ) is Varies trajectory depending on initial position Voltage close to threshold when through V-zero line of the center 4
2. Bifurcation Change attractor depending on parameter Generate periodic attractor by saddle-node bifurcation, saddle-loop bifurcation, etc… Dynamic characteristics of neurons can be explained by bifurcation figure 3. Stochastic Resonance of transition frequency of noise and external signal frequency Weak noise ⇒ Firing does not happen often Strong noise ⇒ Random firing ∴ Firing periodic signal at the size of stable noise 5
• Combination of Neurons combined other neurons by synapse ◦ Types of synapses Direction of signals ⇒ pre-synapse / post-synapse Combined approach ⇒ electrical coupling / chemical coupling Characteristic response ⇒ excitatory / inhibitory 1. Electrical coupling and Chemical coupling ◦ Electrical coupling Two neurons connect directly through gap junction Instantaneous information transfer Difficult to implement plasticity because structure is simple 6
◦ Chemical coupling Neurotransmitter release from pre-synaptic channels Adsorption of post-synaptic receptors Activate ion channels Change membrane potential of synapse Classified as excitatory and inhibitory according to activated ion Slow reaction rate compared to the electrical coupling Various reactions and easy to implement plasticity 2. Synchronization and Anti-Synchronization by Combining Synchronization and anti-synchronization of neurons ⇒Essential to understand the dynamic characteristics of the nervous system Similar currents of neurons, easily synchronize Different currents of neurons, synchronization in strong interaction 7
• Combined Nervous System Function of nervous system determines characteristic of component Understanding function of nervous system as attribute of component 1. Central Pattern Generator (CPG) Generates electrical firing patterns Making biorhythm by stretching muscles. 2. Visual nervous system models Light stimuli Convert to electrical signals Filtering features Synthesis features Associative Memory Recognition Study for filter formation mechanism for extract feature 8
3. Analyze Brain Wave MEG and EEG analyze the dynamic characteristics of the nervous system (MEG: Magnetoencephalogram, EEG: Electroencephalogram) Using the method of time delay, analysis of the original state from scalar time series Clarifying brain waves appear to many states through analysis 9
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