Logical chaotic resonance in the FitzHugh–Nagumo neuron

Yao, Yuangen

doi:10.1007/s11071-021-07155-y

Cited by 22 publications

(4 citation statements)

References 63 publications

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“…[54][55][56][57][58] Chaotic activities in deterministic nonlinear systems can induce chaotic resonance (CR), which is very similar to SR. CR can also be used to amplify or detect weak signals as for SR. Interestingly, chaos can also induce a logic resonance phenomenon (LCR). [59,60] To be specific, if the intensity of chaotic activities is within an optimal window, the reliability of logic operation can be obviously enhanced and the desired logic operation is always achieved. In addition, LCR can be dramatically enhanced via periodic force and coupling between different sub-systems.…”

Section: Introductionmentioning

confidence: 99%

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

Yang¹,

Yao²

2023

Chinese Phys. B

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There exists an optimal range of intensity of chaotic force in which the behaviors of chaos‐driven bistable system with two weak inputs can be consistently mapped to specific logic output. The phenomenon is called logical chaotic resonance (LCR). However, realization of reliable exclusive disjunction (XOR) through LCR has not been reported. Here, we explore the possibility of using chaos to enhance the reliability of XOR logic operation in a triple‐well potential system via LCR. The success probability P of obtaining XOR logic operation can take maximum value 1 in an optimal window of intensity D of chaotic force. Namely, success probability P displays characteristic bell‐shaped behavior by altering intensity of chaos driving force, indicating the occurrence of LCR phenomenon. Further, the effects of periodic force on LCR have been investigated. For subthreshold chaotic force, periodic force with appropriate amplitude and frequency can help to enhance the reliability of XOR logic operation. Thus, LCR can be effectively regulated by changing amplitude and frequency of periodic force.

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Section: Introductionmentioning

confidence: 99%

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

Yang¹,

Yao²

2023

Chinese Phys. B

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“…In 2020, using the same model Nazanin et al [17] studied the different synaptic connections evoke different firing patterns in neurons subjects to electromagnetic field then, shown that electrochemical synapses provided richer dynamical behaviors compared to electrical or chemical synapses. Also, in the beginning of 2022 Yao [18] demonstrated that the chaos-driven FHN neuron can reliably function as logic gate. Toward the end of the same year, Bao et al [19] enriched the literature with the memristive synape-based neural network with simplest cyclic connection able to exhibit coexisting attractors made up of stable points and unstable periodic or chaotic orbits.…”

Section: Introductionmentioning

confidence: 99%

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

Balaraman,

Nzoulewa Dountsop,

Kengne

et al. 2023

Phys. Scr.

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This work investigates the dynamics and implementation of a three inertia circulant neurons model with each neuron activated by a non-monotonic Crespi function. Owing its source to the work previously done by Z. Song and co-authors[1], we proposes a network made up of three neurons connected cyclically. Z. Song and collaborators studied the dynamics of an inertia neural system and demonstrated the mixed coexistence of periodic orbits and chaotic attractors but they show the coexistence of only two and four attractors. Recently, B.F.Boya and co-workers[2] break the symmetry of the previous system then, demonstrated the coexistence of two, three, four and six attractors. Here, is analyzed a model capable of the coexisting of two, three, four, six, eight and ten attractors basing on different starting points. Analytically, the system is dissipative and presents fifteen equilibrium unstable for a given rank of parameters. This is the reason of the demonstration of Hopf bifurcation in the model when the bifurcation parameter is the first synaptic weight. Also, using bifurcation diagrams, Maximum Lyapunov Exponent diagram, phase portraits, two parameters Lyapunov diagrams, double-side Poincaré section and basin of attraction, intriguing phenomena have been demonstrated such as hysteresis, coexistence of parallel branches of bifurcation, antimonotonicity to name these few. Moreover, offset boosting is exhibiting associated once with transient oscillation leading from one chaotic state to another which is an input to the dynamics of inertia neural systems particularly and chaotic system in general. A number of coexisting attractors have been developed by the new network which can be used to build sophisticated cryptosystem or to explain the possible tasks of a brain in normal or abnormal cases. In other to emphasize the feasibility of the model, a microcontroller-based implementation has been applied to demonstrate the period-doubling route to chaos obtained numerically.

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“…This phenomenon is named logical stochastic resonance (LSR) [26]. In fact, by virtue of aforementioned resonance mechanism including SR, coherence resonance, and chaotic resonance, stochastic noise or some other non-stochastic elements such as periodic force [48][49][50][51][52], chaotic force [53][54][55][56], time delay [57][58][59][60], parameter [61], coupling [62,63], etc. can be used to improve the reliability of logic systems even in the case that the input logic signal is subthreshold one.…”

Section: Introductionmentioning

confidence: 99%

“…This new type of logical elements may be energy-saving since it can work reliably under the subthreshold inputs, so it has aroused wide concern and has a promising prospect in energy-efficient computing building modules of futuristic computational systems. What is particularly worth mentioning about logical resonance is that we have recently proposed the concept of logical chaotic resonance (LCR) based on a bistable system [53] and LCR have been successfully extended to the two-state excitable Fitzhugh-Nagumo (FHN) neuron model [56]. Many previous studies have shown that autapse significantly affects the firing patterns and the resonance dynamics of neurons.…”

Section: Introductionmentioning

confidence: 99%

Autapse-induced logical resonance in the FitzHugh–Nagumo neuron

Yao

2022

Nonlinear Dyn

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It was demonstrated that the chaos-driven FitzHugh-Nagumo (FHN) neuron can be considered as a logic system to implement the reliable logic operation through logical resonance. Signal transmission between neurons is dependent on an essential component called synapse. Autapse (meaning the self-synapse) widely exists in various kinds of neurons, and it significantly affects the neuronal dynamics and functionalities. However, the effects of autapse on logical resonance have not been reported yet. Here, we explore the effects of autapse on the reliability of logical operation based on the autaptic FHN neuron with time-dependent coupling intensity. Our results demonstrate that there are the optimal ranges of autaptic time delay , the amplitude and frequency of coupling intensity, and phase fluctuation at which the reliability of logical operation can be maximized. That is, autapse-induced logical resonance can be realized in the autaptic FHN neuron. More interestingly, multiple logical resonance can be observed by regulating time delay, frequency ratio between oscillating coupling intensity and external input, and phase fluctuation. The results presented here provide the novel phenomena, and may have implications in understanding the logic gate-like functionalities in the nervous systems.

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Logical chaotic resonance in the FitzHugh–Nagumo neuron

Cited by 22 publications

References 63 publications

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

Autapse-induced logical resonance in the FitzHugh–Nagumo neuron

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