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

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

The Geometry of Plasticity-Induced Sensitization in Isoinhibitory Rate Motifs

A well-known phenomenon in sensory perception is desensitization, wherein behavioral responses to persistent stimuli become attenuated over time. In this letter, our focus is on studying mechanisms through which desensitization may be mediated at the network level and, specifically, how sensitivity changes arise as a function of long-term plasticity. Our principal object of study is a generic isoinhibitory motif: a small excitatory-inhibitory network with recurrent inhibition. Such a motif is of interest due to its overrepresentation in laminar sensory network architectures. Here, we introduce a sensitivity analysis derived from control theory in which we characterize the fixed-energy reachable set of the motif. This set describes the regions of the phase-space that are more easily (in terms of stimulus energy) accessed, thus providing a holistic assessment of sensitivity. We specifically focus on how the geometry of this set changes due to repetitive application of a persistent stimulus. We find that for certain motif dynamics, this geometry contracts along the stimulus orientation while expanding in orthogonal directions. In other words, the motif not only desensitizes to the persistent input, but heightens its responsiveness (sensitizes) to those that are orthogonal. We develop a perturbation analysis that links this sensitization to both plasticity-induced changes in synaptic weights and the intrinsic dynamics of the network, highlighting that the effect is not purely due to weight-dependent disinhibition. Instead, this effect depends on the relative neuronal time constants and the consequent stimulus-induced drift that arises in the motif phase-space. For tightly distributed (but random) parameter ranges, sensitization is quite generic and manifests in larger recurrent E-I networks within which the motif is embedded.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.