相关论文: Synchronization of Boundary Coupled Hindmarsh-Rose…

By using a semi-analytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of…

Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this…

In this work we studied the combined action of chemical and electrical synapses in small networks of Hindmarsh-Rose (HR) neurons on the synchronous behaviour and on the rate of information produced (per time unit) by the networks. We show…

We propose a working hypothesis supported by numerical simulations that brain networks evolve based on the principle of the maximization of their internal information flow capacity. We find that synchronous behavior and capacity of…

Hodgkin-Huxley equations as a monumental breakthrough in biological and physiological theory of the 20th century had been distilled into many simplified models to study, typically FitzHugh-Nagumo equations and Hindmarsh-Rose equations, but…

This paper deals with synchronization of a class of infinite-dimensional systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs,…

The response of a neuron to synaptic input strongly depends on whether or not it has just emitted a spike. We propose a neuron model that after spike emission exhibits a partial response to residual input charges and study its collective…

We report a new mechanism through which extreme events with a dragon king-like distribution emerge in a network of unidirectional ring of Hindmarsh-Rose bursting neurons interacting through chemical synapses. We establish and substantiate…

The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…

In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR…

A novel viewpoint, i.e., adaptive synchronization, is proposed to explore collective rhythm observed in many complex, self-organizing systems. We show that a simple adaptive coupling is able to tip arrays of oscillators towards collective…

In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…

The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the…

Temporal correlations in the brain are thought to have very dichotomic roles. On one hand they are ubiquitously present in the healthy brain and are thought to underlie feature binding during information processing. On the other hand large…

Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks…

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the…

Synchronization is studied in a spatially-distributed network of weekly-coupled, excitatory neurons of Hodgkin-Huxley type. All neurons are coupled to each other synaptically with a fixed time delay and a coupling strength inversely…

For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of…

The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…

We study a modification of the canonical model for networks of class I neurons, presented by Hoppensteadt and Izhikevich, in which the 'pulse' emitted by a neuron is smooth rather than a delta-function. We prove two types of results about…