Synaptic changes modulate spontaneous transitions between tonic and bursting neural activities in coupled Hindmarsh-Rose neurons

Alternating chimera states and synchronization in multilayer neuronal networks with ephaptic intralayer coupling

Over the past decade, most of researches on the communication between the neurons are based on synapses. However, the changes in action potentials in neurons may produce complex electromagnetic fields in the media, which may also have an impact on the electrical activity of neurons. To explore this factor, we construct a two-layer neuronal network composed of identical Hindmarsh-Rose neurons. Each neuron is connected with its neighbors in the layer via magnetic connections and a neuron in the corresponding position of the other layer via electrical synapse. By adjusting the electrical coupling strength and magnetic coupling strength, we find the appearance of alternating chimera states and transient chimera states whenever the intralayer coupling is nonlocal and local, respectively. According to our study, these phenomena have not been studied in multilayer networks of this structure. And it is found that the transient chimera states only could occur when the number of coupled neighbors is small. In addition, the states of two independent networks will affect the final states of networks applying the same sufficiently large interlayer coupling strength. Our study reveals a possible effect of electrical coupling and ephaptic coupling produced together on the dynamic behavior of the neuronal networks. Meanwhile, our results suggest that it makes sense to take electromagnetic induction into neuronal models.

Coexistence of infinitely many patterns and their control in heterogeneous coupled neurons through a multistable memristive synapse

The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This phenomenon is investigated in this contribution using a model of a 2D FitzHugh-Nagumo neuron coupled with a 3D Hindmarsh-Rose neuron through a multistable memristive synapse. The investigation of the equilibria revealed that the coupled neuron model is equilibrium free and, thus, displays a hidden dynamics. Some traditional nonlinear analysis tools are used to demonstrate that the heterogeneous neuron system is able to exhibit the coexistence of an infinite number of electrical activities involving both periodic and chaotic patterns. Of particular interest, a noninvasive control method is applied to suppress all the periodic coexisting activities, while preserving only the desired chaotic one. Finally, an electronic circuit of the coupled neurons is designed in the PSpice environment and used to further support some results of the theoretical investigations.