Efficient synchronization of structurally adaptive coupled Hindmarsh–Rose neurons

Abstract

The use of spikes to carry information between brain areas implies complete or partial synchronization of the neurons involved. The degree of synchronization reached by two coupled systems and the energy cost of maintaining their synchronized behaviour is highly dependent on the nature of the systems. For non-identical systems the maintenance of a synchronized regime is energetically a costly process. In this work, we study conditions under which two non-identical electrically coupled neurons can reach an efficient regime of synchronization at low energy cost. We show that the energy consumption required to keep the synchronized regime can be spontaneously reduced if the receiving neuron has adaptive mechanisms able to bring its biological parameters closer in value to the corresponding ones in the sending neuron.

Suppression of firing activities in neuron and neurons of network induced by electromagnetic radiation

“…As a statistical explanation for the propagating wave of the neuronal collective electric activities, we introduced a synchronization factor [30][31][32], discussed in Eq. (17)- (19), where R = 1 means that v i j are in a perfect synchronization state and R = 0 denotes a complete de-synchronization state.…”

“…In this paper, we focused on accomplishing the translation between the absorbed power of electromagnetic radiation and the polarizing current in neuronal soma with a mathematical method based on the neuronal Hodgkin-Huxley electrical circuit [25][26][27][28] and the differential model of energy cost of this electrical circuit [29][30][31][32]. We simulated the process of neuron absorbing power from electromagnetic radiation, and an additional current, translated from this absorbed power, was applied to the Hodgkin-Huxley model.…”

A new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons

“…Remark 2 Compared with synchronization results in [10], [11], [12], [13], [14], and [15], there is no external control in the neuron (2).…”

“…Similar to master and slave synchronization of neural networks and chaotic systems [4], [5], [6], synchronization of two coupled HR neurons (master and slave neurons) has attracted increasing attention [7], [8], [9]. Several papers consider how to design the external control in one neuron, including linear feedback control, adaptive control, or other nonlinear control to achieve the synchronization of two coupled HR neurons [10], [11], [12], [13], [14], [15]. However, external control in one neuron may be very difficult even impossible to be realized [16] from the theory of neuroscience and molecular biology.…”

Synchronization for time-varying complex dynamical networks with different-dimensional nodes and non-dissipative coupling

“…Let the i -th node be the following four-dimensional HR neuron [30]: ( 2 3 4 3 3 3 1 3 3 2 4 2 2 2 1 2 3 2 3 1 2 1 2 , and i I is a external current input of the i-th node, respectively [30].…”