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

In this paper, bidirectional-coupled neurons through an asymmetric electrical synapse are investigated. These coupled neurons involve 2D Hindmarsh-Rose (HR) and 2D FitzHugh-Nagumo (FN) neurons. The equilibria of the coupled neurons model are investigated, and their stabilities have revealed that, for some values of the electrical synaptic weight, the model under consideration can display either self-excited or hidden firing patterns.

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.

A new oscillator with mega-stability and its Hamilton energy: Infinite coexisting hidden and self-excited attractors.

In this paper, we introduce an interesting new megastable oscillator with infinite coexisting hidden and self-excited attractors (generated by stable fixed points and unstable ones), which are fixed points and limit cycles stable states. Additionally, by adding a temporally periodic forcing term, we design a new two-dimensional non-autonomous chaotic system with an infinite number of coexisting strange attractors, limit cycles, and torus. The computation of the Hamiltonian energy shows that it depends on all variables of the megastable system and, therefore, enough energy is critical to keep continuous oscillating behaviors.