Hopf bifurcation in the evolution of networks driven by spike-timing-dependent plasticity

Abstract

We study the interplay of topology and dynamics in a neural network connected with spiketiming-dependent plasticity (STDP) synapses. Stimulated with periodic spike trains, the STDPdriven network undergoes a synaptic pruning process and evolves to a residual network. We examine the variation of topological and dynamical properties of the residual network by varying two key parameters of STDP: Synaptic delay and the ratio between potentiation and depression.Our extensive numerical simulations of the Leaky Integrate-and-Fire model show that there exists two regions in the parameter space. The first corresponds to fixed point configurations, where the distribution of peak synaptic conductances and the firing rate of neurons remain constant over time. The second corresponds to oscillating configurations, where both topological and dynamical properties vary periodically which is a result of a fixed point becoming a limit cycle via a Hopf bifurcation. This leads to interesting questions regarding the implications of these rhythms in the topology and dynamics of the network for learning and cognitive processing.

Combined effects of STDP and homeostatic structural plasticity on coherence resonance

“…To prevent unbounded growth, negative conductances (i.e., negative coupling strength), and elimination of synapses (i.e., g ij = 0), we set a range with the lower and upper bounds: g ij ∈ [g min , g max ] = [0.0001, 0.35], where g max = 0.35 mS/cm 2 is in the range of the maximum synaptic conductances [0.3,0.5] mS/cm 2 usually measured in the standard Hodgkin-Huxley neuron [76,77], and the lower bound g min = 0.0001 is set to ensure not to miss any effects that occur outside of classical parameter ranges. Moreover, the initial weight of all excitable synapses is normally distributed in the interval [g min , g max ], with mean g 0 = 0.185 and standard deviation σ 0 = 0.02.…”

Adaptive stochastic resonance in self-organized small-world neuronal networks with time delay

“…Experimental researches show that the functional structures in the brain can be remapped through STDP, which is prevalently reorganized into both small-world and scale-free networks [37,38]. More recently, modelling studies on functional role of STDP in neural dynamics have gained increasing interest [39][40][41]. For example, Lee et al use a simplified biophysical model of a cortical network with STDP, which provides a mechanism for potentiation and depression depending on input frequency, and suggest that the slow NMDAR current decay helps to regulate the optimal amplitude and duration of the plasticity [42].…”

Optimal Resonances in Multiplex Neural Networks Driven by an STDP Learning Rule

“…It was found that small learning rates lead to more robust learning [32]. Hence, in this work, we choose a small learning rate (i.e., λ = 0.0001) which, by the way, also simulates the effect of STDP on the long-term evolution of a neural network [37]. In the numerical simulations, we will consider eSTDP with an asymmetric Hebbian time window for the synaptic modifications given by [4,22]:…”