Chimera State in the Network of Fractional‐Order FitzHugh–Nagumo Neurons

Abstract

The fractional calculus in the neuronal models provides the memory properties. In the fractional-order neuronal model, the dynamics of the neuron depends on the derivative order, which can produce various types of memory-dependent dynamics. In this paper, the behaviors of the coupled fractional-order FitzHugh–Nagumo neurons are investigated. The effects of the coupling strength and the derivative order are under consideration. It is revealed that the level of the synchronization is decreased by decreasing the derivative order, and the chimera state emerges for stronger couplings. Furthermore, the patterns of the formed chimeras rely on the order of the derivatives.

Spiral wave dynamics in a neuronal network model

“…Chimera states play an important role in empirical brain networks, specially in the cerebral cortex [12]. It has been found in networks composed of coupled neurons, such as integrate-and-fire [13,14], Hodgkin-Huxley [9], Hindmarsh-Rose [15], FitzHugh-Nagumo [16,17], Morris-Lecar [18], Nekorkin maps [19] and others. The spatiotemporal patterns, in which coherence coexists with incoherence, have been reported in local [20,21] and non-local network configurations [22,23].…”

“…Chemical and electrical synapses can affect the features of chimera states and traveling waves [26]. The coexistence of patterns can emerge due to electrical and chemical coupling in a multi-weighted of the memristive Fitzhugh-Nagumo network [16]. It was demonstrated the importance of such interactions to obtain synchronous and desynchronous behaviors coexisting [27].…”

Multistability route in a PWL multi-scroll system through fractional-order derivatives

“…With the recent increase of studies and experiments with fractional order systems, the possibilities of finding new behaviors and better descriptions of natural phenomena are a recurring theme in the literature [22][23][24][25][26][27][28][29][30]. However, the use of this numerical tool has been neglected because it is used as a dynamical validation mechanism and the effects and physical implications associated with the use of fractional order derivatives are ignored.…”

Lag Synchronization of Noisy and Nonnoisy Multiple Neurobiological Coupled FitzHugh–Nagumo Networks with and without Delayed Coupling

“…In past research, researchers have investigated the interaction between neurons and their networks in different brain regions using techniques like neuroimaging systems [ 56 – 59 ] and used computational models to predict the complex dynamics of neurons [ 60 , 61 ] and showed that noise plays an important role in the dynamical functionality of the neurons and their networks [ 62 , 63 ]. The fundamentals of the noise and delay in the communication of neuronal networks are still ubiquitous but they have a very strong implication for the functionality of neurons and their networks and in general, the synchronized functionality of the brain [ 64 , 65 ].…”