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This paper studies the dynamical behaviors of a pair of FitzHugh-Nagumo neural networks with bidirectional delayed couplings. It presents a detailed analysis of delay-independent and delay-dependent stabilities and the existence of bifurcated oscillations. Illustrative examples are performed to validate the analytical results and to discover interesting phenomena. It is shown that the network exhibits a variety of complicated activities, such as multiple stability switches, the coexistence of periodic and quasi-periodic oscillations, the coexistence of periodic and chaotic orbits, and the coexisting chaotic attractors.
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http://dx.doi.org/10.1063/1.5000854 | DOI Listing |
Chaos
March 2025
Department of Physics, Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente, 225-22451-900 Gávea, Rio de Janeiro, RJ, Brazil.
Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this work, we examine a simple "toy model" of an excitable medium, a linear chain of diffusely coupled FitzHugh-Nagumo neurons, and analyze the transmission of a sinusoidal signal injected into one of the neurons at the ends of the chain.
View Article and Find Full Text PDFACS Omega
February 2025
Unconventional Computing Laboratory, University of the West of England, Bristol BS16 1QY, U.K.
Proteinoids, or thermal proteins, are produced by heating amino acids. Proteinoids form hollow microspheres in water. The microspheres produce oscillation of electrical potential.
View Article and Find Full Text PDFCogn Neurodyn
December 2024
Center for Research, SRM Institute of Science and Technology-Ramapuram, Chennai, India.
In this study, we investigate the impact of first and second-order coupling strengths on the stability of a synchronization manifold in a Discrete FitzHugh-Nagumo (DFHN) neuron model with memristor coupling. Master Stability Function (MSF) is used to estimate the stability of the synchronized manifold. The MSF of the DFHN model exhibits two zero crossings as we vary the coupling strengths, which is categorized as class .
View Article and Find Full Text PDFCogn Neurodyn
October 2024
School of Electrical Information and Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002 China.
In this paper, a cosine hyperbolic memristor model is proposed with bistable asymmetric hysteresis loops. A neural network of coupled hyperbolic memristor is constructed by using the Fitzhugh-Nagumo model and the Hindmarsh-Rose model. The coupled neural network with a large number of equilibrium points is obtained by numerical analysis.
View Article and Find Full Text PDFChaos
December 2024
Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia.
We present numerical results on the effects of two presynaptic FitzHugh-Nagumo neurons on a postsynaptic neuron under unidirectional electrical coupling. The presynaptic neurons affect the postsynaptic neuron not simultaneously but with a certain time shift. We consider cases where the amplitudes of the presynaptic spikes can be both higher and lower than the excitation threshold level.
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