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

Abstract

Chaotic resonance (CR) is a new phenomenon induced by an intermediate level of chaotic signal intensity in neuronal systems. In the current study, we investigated the effects of autapse on the CR phenomenon in single neurons and small-world (SW) neuronal networks. In single neurons, we assume that the neuron has only one autapse modelled as electrical, excitatory chemical and inhibitory chemical synapse, respectively. Then, we analysed the effects of each one on the CR, separately. Obtained results revealed that, regardless of its type, autapse significantly increases the chaotic resonance of the appropriate autaptic parameter’s values. It is also observed that, at the optimal chaotic current intensity, the multiple CR emerges depending on autaptic time delay for all the autapse types when the autaptic delay time or its integer multiples match the half period or period of the weak signal. In SW networks, we investigated the effects of chaotic activity on the prorogation of pacemaker activity, where pacemaker neurons have different kinds of autapse as considered in single neuron cases. Obtained results revealed that excitatory and electrical autapses prominently increase the prorogation of pacemaker activity, whereas inhibitory autapse reduces or does not change it. Also, the best propagation was obtained when the autapse was excitatory. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

Vibrational and stochastic resonances in driven nonlinear systems: part 2

“…These are attributed mainly to the slow, long-time variation in neuronal excitability that can be significantly influenced by astrocytic calcium oscillations when the astrocytic Ca 2+ dynamics are appropriately adjusted. Baysal et al [29] examine the impact of an autapse on chaotic resonance (CR) in single neurons as well as on small-world neuronal networks. An autapse is a special kind of synaptic contact, either electrical or chemical, connecting the axon of a neuron onto its own dendrites.…”

“…While a few articles in part 1 presented analysis on position-dependent mass systems [ 21 ], delayed feedback-induced resonances in deformable potential system [ 22 ] and Duffing oscillator [ 23 ], and driven two-level quantum systems [ 24 ], part 2 assembles state-of-the-art, original contributions on VR and SR in some systems not covered by part 1. These include a Brownian particle confined in a structural cavity [ 25 , 26 ], coupled neuron-astrocyte [ 27 ] systems and neural networks [ 28 , 29 ]. Part 2 also presents articles in four application domains: image perception [ 6 ], energy harvesting [ 8 ], control of aerodynamic instability [ 12 ], and vibrational machines and devices [ 30 ].…”

“…More importantly, driven nonlinear systems often form elements of complex networks, so that the impacts of the collective dynamics arising from network interactions on the response to the driving forces of an individual system should not be overlooked. In this part, there are two papers on complex networks—one of these reviews the enhancement of weak signals in complex networks due to stochastic and vibrational resonances [ 28 ], while the second article considers the effects of different kinds of autapses in the chaotic response of a single neuron and a network [ 29 ].…”

“… Vibrational resonance in a neuron–astrocyte coupled model, by Calim et al [ 27 ]. Impacts of autapse on chaotic resonance in single neurons and small-world neuronal networks, by Baysal et al [ 29 ]. Characterizing stochastic resonance in a triple cavity, by Mei et al [ 26 ].…”

“…Impacts of autapse on chaotic resonance in single neurons and small-world neuronal networks, by Baysal et al [ 29 ].…”