Asymmetry in electrical coupling between neurons alters multistable firing behavior

Abstract

The role of asymmetry in electrical synaptic connection between two neuronal oscillators is studied in the Hindmarsh-Rose model. We demonstrate that the asymmetry induces multistability in spiking dynamics of the coupled neuronal oscillators. The coexistence of at least three attractors, one chaotic and two periodic orbits, for certain coupling strengths is demonstrated with time series, phase portraits, bifurcation diagrams, basins of attraction of the coexisting states, Lyapunov exponents, and standard deviations of peak amplitudes and interspike intervals. The experimental results with analog electronic circuits are in good agreement with the results of numerical simulations.

Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue

“…92,93 Such switching between different spatial activity patterns, which can be intermittent, has recently been modelled by networks of FitzHugh-Nagumo units 94 or MorrisLecar neurons. 95 In this issue, Pisarchik et al 96 suggest a possible mechanism for the intermittent character of neurophysiological data. The origin of such a behavior can lie in multistability induced by an asymmetry in the electrical coupling between neurons.…”

Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons

“…Besides the above-mentioned advances, investigation of the coupled neurons has also attracted a lot of attention. For example, Pisarchik et al (Pisarchik et al 2018 ) explored the dynamics of two identical 3D HR coupled models through an asymmetric electrical coupling. The result indicated that the 6D neuronal oscillator obtained was able to exhibit the phenomenon of multistability with up to six firing activities.…”

Stochastic Memristive Interface for Neural Signal Processing

“…The history of neuromorphic technologies began in the late 1980s with the emergence of computation machines, and since then, significant advances have been achieved in elec-Sensors 2021, 21, 5587 2 of 12 tronics, physics of micro-and nanostructures, and solid-state nanoelectronics. The careful development of neuron-like electrical circuits made it possible to reproduce basic neural behaviors, such as resting, spiking, and bursting dynamics, as well as more sophisticated regimes, including chaos and multistability [21][22][23][24][25].…”