Chaotic resonance in Hodgkin–Huxley neuron

Transition of Neural Activity From the Chaotic Bipolar-Disorder State to the Periodic Healthy State Using External Feedback Signals

“…Similar to the synchronization phenomenon of stochastic resonance, in chaotic resonance, the synchronization to a weak input signal is enhanced by the internal chaotic dynamics instead of additive noise (reviewed in Anishchenko et al, 2007 ; Rajasekar and Sanjuán, 2016 ). Chaotic resonance has been widely studied in many types of systems, including neural systems (Nishimura et al, 2000 ; Nobukawa and Nishimura, 2016 ; Nobukawa et al, 2016 , 2017 ; Baysal et al, 2019 ; reviewed in Nobukawa and Nishimura, 2020 ). In these fluctuation-enhanced synchronization phenomena, the strength of the external perturbation required for the development of a periodic state is weaker than that required for forced oscillations (Sinha, 1999 ; reviewed in Pikovsky et al, 2003 ; Anishchenko et al, 2007 ; Rajasekar and Sanjuán, 2016 ).…”

Impacts of autapse on chaotic resonance in single neurons and small-world neuronal networks

“…The possibility of gates being open for the sodium activation, sodium inactivation and potassium activation is expressed by m , n , h respectively, and change over time according to the below equation [28]. dγdt=αγfalse(Vfalse)false(1−xfalse)−βγfalse(Vfalse)γ,1emγ=m,n,h. The αγ and βγ are rate functions of gate variables and change dependent on cell membrane potential [27]. I chaos = ϵx denotes the current which is assumed to be caused by the chaotic activities of environmental neurons.…”

“…ϵ represents the chaotic current intensity, and x is external chaotic signal source based on the Lorenz system. The Lorenz system used for producing the chaotic signal is given by equation (2.5) [27,31]. dxdt=σfalse(y−xfalse), dydt=px−y−xz, dzdt=xz−λz. The Q factor, which is the Fourier series coefficient calculated at the frequency of the applied weak signal, is used to measure numerically the effect of the chaotic activity on CR phenomenon.…”

“…Baysal et al . [27] also showed that chaotic activity plays an active role in weak signal coding in H–H neurons. In many studies, effects of autapse on stochastic resonance and wave formation are investigated on single neuron levels and in complex network topologies [11–14].…”

Multiple Firing Patterns in Coupled Hindmarsh-Rose Neurons with a Nonsmooth Memristor

“…These neuron models have demonstrated different electrical activities and attracted many researchers' attention. For example, the FHN neuron model exhibits discontinuous transition between different oscillations [ 7 ] and double coherence resonance induced by phase noise [ 8 ]; the HH neuron model displays evoking spiking caused by enough noise intensity [ 9 ], chaotic resonance dependent on current intensity [ 10 ], and extrinsic stochastic resonance caused by ion shot noise [ 11 ]; in the presence of periodic input, the HR neuron model can show nonlinear resonance behavior [ 12 ], periodic and chaotic firing patterns [ 13 ], transition between chaotic firing and periodic firing [ 14 ], and bursting phenomenon [ 15 ]; the Izhikevich neuron model can appear chaotic resonance [ 16 , 17 ]; the ML neuron model can exhibit mono- and bistable dynamic regimes [ 18 ] and responses to two temperature-sensitive ion channels, calcium and leak current, respectively [ 19 ]. These classical models and their dynamical analysis are motivating researchers to develop more realistic or refined neuron models.…”