1. Globally-Coupled Excitatory Izhikevich Neurons Coupling-Induced Population Synchronization in An Excitatory Population of Subthreshold Izhikevich Neurons Woochang Lim 1 and Sang-Yoon Kim 2 1 Department of Science Education, Daegu National University of Education 2 Research Department, LABASIS Co. Summary  Appearance of Rich Population States by Changing the Coupling Strength Incoherent State  Spike Synchronization  Burst Synchronization  Incoherent State  Fast Spike Synchronization  Incoherent State  Non-firing State  Emergence of Three Types of Population Synchronization Spike, Burst, and Fast Spike Synchronization  Future Works: Brain Rhythm Emerging via Population Synchronization in the Complex Neural Network such as Small-World and Scale-Free Neural Networks Transition to Non-Firing State via Stochastic Oscillator Death  Average Population Spike Rate R As N  then R  non-zero (zero) limit value for firing (non-firing) states. Non-firing states appear due to the stochastic oscillator of individual neurons Various Transitions in Individual Behaviors  Transition from Spiking to Bursting As J increases, average number of spike per burst becomes larger than unity.  Transition from spiking to bursting With further increase in J, increases.  Transition from Bursting to Fast Spiking With increase in J, burst length becomes longer Eventually average burst length divers to the infinity.  Transition to the Fast Spiking State  Transition from Fast Spiking to Oscillator Death As J increases, slow spikings with longer spiking phases appear and mean firing rate goes to zero.  Occurrence of Stochastic Oscillator Death Population Coherent and Incoherent States  Appearance of Rich Population States by Changing the Coupling Strength Global Potential V G & Global Recovery Variable U G : Incoherent State  Spike Synchronization  Burst Synchronization  Incoherent State  Fast Spike Sync.  Incoherent State  Non-firing State  Thermodynamic Order Parameter Mean Square Deviation of V G : As N  then O  non- zero (zero) limit value for coherent (incoherent) states. Three Types of Population Synchronization  Spike Synchronization  Burst Synchronization Stripes appear regularly Clear burst bands, composed of stripes, in the raster plot. appear successively. V G shows a small-amplitude V G exhibits a large-amplitude bursting rhythm. Rhythms.  Fast Spike Synchronization Stripes appear successively at short time interval in the raster plot. V G shows a small-amplitude fast rhythm. Introduction  Brain Rhythm Emerging via Population Synchronization Brain Rhythm emerge via synchronization between individual firings. Population Synchronization between neural firings may be used for efficient sensory and cognitive processing. Population Synchronization is also correlated with pathological rhythms associated with neural diseases.  Population Synchronization in Neural Network of Suprathreshold Neurons Individual Neurons: Regular Firings like Clocks  Population Synchronization in Neural Network of Subthreshold Neurons Individual Neurons: Intermittent and Stochastic Firings like Geiger Counters Noise-Induced Population Synchronization in a Population of Subthreshold Neurons Regular-Spiking (RS) Cortical Excitatory Neuron  Firing Transition in the Single Izhikevich Neuron Transition to firing occurs I DC =I* DC (~3.78) RS Izhikevich neuron shows type-II excitability. I DC I* DC : Spiking state  Complex Noise-induced Spiking with Irregular Interspike Intervals in the Subthreshold Izhikevich Neuron for I DC =3.6 Parameters for regular-spiking cortical excitatory neuron: a=0.02, b=0.2, c=-65, d=8 Parameters for excitatory synapse:  =10,  =0.5, V syn =10, v*=0,  =2