Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network

We consider a two-layer multiplex network of diffusively coupled FitzHugh-Nagumo (FHN) neurons in the excitable regime. It is shown, in contrast to SISR in a single isolated FHN neuron, that the maximum noise amplitude at which SISR occurs in the network of coupled FHN neurons is controllable, especially in the regime of strong coupling forces and long time delays. In order to use SISR in the first layer of the multiplex network to control CR in the second layer, we first choose the control parameters of the second layer in isolation such that in one case CR is poor and in another case, non-existent. It is then shown that a pronounced SISR cannot only significantly improve a poor CR, but can also induce a pronounced CR, which was non-existent in the isolated second layer. In contrast to strong intra-layer coupling forces, strong inter-layer coupling forces are found to enhance CR. While long inter-layer time delays just as long intra-layer time delays, deteriorates CR. Most importantly, we find that in a strong inter-layer coupling regime, SISR in the first layer performs better than CR in enhancing CR in the second layer. But in a weak inter-layer coupling regime, CR in the first layer performs better than SISR in enhancing CR in the second layer. Our results could find novel applications in noisy neural network dynamics and engineering

Synchronization in STDP-driven memristive neural networks with time-varying topology

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing $P$ (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing $F$ (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay $\tau_c$, the average degree $\langle k \rangle$, and the rewiring probability $\beta$ have some appropriate values. When $\tau_c$, $\langle k \rangle$, and $\beta$ are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when $F$ increases, depending on the network topology. It is also found that the time delay $\tau_c$ can induce intermittent CS and PS whose occurrence is independent $F$. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.Comment: 28 pages, 86 references, 8 figures, 2 Table

Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses

Electrical and chemical synapses shape the dynamics of neural networks and their functional roles in information processing have been a longstanding question in neurobiology. In this paper, we investigate the role of synapses on the optimization of the phenomenon of self-induced stochastic resonance in a delayed multiplex neural network by using analytical and numerical methods. We consider a two-layer multiplex network, in which at the intra-layer level neurons are coupled either by electrical synapses or by inhibitory chemical synapses. For each isolated layer, computations indicate that weaker electrical and chemical synaptic couplings are better optimizers of self-induced stochastic resonance. In addition, regardless of the synaptic strengths, shorter electrical synaptic delays are found to be better optimizers of the phenomenon than shorter chemical synaptic delays, while longer chemical synaptic delays are better optimizers than longer electrical synaptic delays -- in both cases, the poorer optimizers are in fact worst. It is found that electrical, inhibitory, or excitatory chemical multiplexing of the two layers having only electrical synapses at the intra-layer levels can each optimize the phenomenon. And only excitatory chemical multiplexing of the two layers having only inhibitory chemical synapses at the intra-layer levels can optimize the phenomenon. These results may guide experiments aimed at establishing or confirming the mechanism of self-induced stochastic resonance in networks of artificial neural circuits, as well as in real biological neural networks.Comment: 24 pages, 7 figure

Dynamics of neural fields with exponential temporal kernel

Various experimental methods of recording the activity of brain tissue in vitro and in vivo demonstrate the existence of traveling waves. Neural field theory offers a theoretical framework within which such phenomena can be studied. The question then is to identify the structural assumptions and the parameter regimes for the emergence of traveling waves in neural fields. In this paper, we consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging Spatio-temporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations, in contrast to the Green's function used by Atay and Hutt (SIAM J. Appl. Math. 65: 644-666, 2004). However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which the Green's function does not. Through a dynamic bifurcation analysis, we give explicit Hopf (temporally non-constant, but spatially constant solutions) and Turing-Hopf (spatially and temporally non-constant solutions, in particular traveling waves) bifurcation conditions on the parameter space which consists of the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.Comment: 25 pages, 8 Figures, 44 Reference

A simple parameter can switch between different weak-noise–induced phenomena in a simple neuron model

In recent years, several, apparently quite different, weak-noise–induced resonance phenomena have been discovered. Here, we show that at least two of them, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR), can be related by a simple parameter switch in one of the simplest models, the FitzHugh-Nagumo (FHN) neuron model. We consider a FHN model with a unique fixed point perturbed by synaptic noise. Depending on the stability of this fixed point and whether it is located to either the left or right of the fold point of the critical manifold, two distinct weak-noise–induced phenomena, either SISR or ISR, may emerge. SISR is more robust to parametric perturbations than ISR, and the coherent spike train generated by SISR is more robust than that generated deterministically. ISR also depends on the location of initial conditions and on the time-scale separation parameter of the model equation. Our results could also explain why real biological neurons having similar physiological features and synaptic inputs may encode very different information

Coherence resonance and stochastic synchronization in a small-world neural network: An interplay in the presence of spike-timing-dependent plasticity

Coherence resonance (CR), stochastic synchronization (SS), and spike-timing-dependent plasticity (STDP) are ubiquitous dynamical processes in biological neural networks. This ubiquitousness should permit (or even condemn) these phenomena to interact with an interplay that should enable the brain to make synergistic and optimal use of these phenomena to possess such an impressive information processing capability. Whether enhancing CR can be associated with improving SS and vice versa is, thus, a fundamental question of interest. STDP and different network connectivity effects on this enhancement interplay are still elusive. This paper considers a small-world network of excitable Hodgkin-Huxley neurons driven by channel noise and STDP with an asymmetric Hebbian time window. Numerical results indicate that there exist specific intervals of parameter values of the network topology and the STDP learning rule in which CR and SS can be simultaneously enhanced. Our results imply that the inherent noise and STDP rule in neural networks can jointly play a constructive or antagonistic role in enhancing spatio-temporal coherence in neural activity.Comment: 13 pages, 12 figures, 70 reference