A chaotic system with equilibria located on a line and its fractional-order form

Rajagopal, Karthikeyan; Nazarimehr, Fahimeh; Bahramian, Alireza; Jafari, Sajad

doi:10.1016/b978-0-32-390090-4.00007-x

Cited by 1 publication

(1 citation statement)

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“…They enable the highlighting of the dynamical behavior exhibited by a neuron or neural network as self-excited or hidden. Let us recall that self-excited attractors are generated from a nonlinear dynamical system with unstable equilibria [38,39]. In contrast, hidden attractors are generated from systems without equilibria or systems with state equilibria [40][41][42].…”

Section: Rest Points and Their Stabilitymentioning

confidence: 99%

Emerging Spiral Waves and Coexisting Attractors in Memductance-Based Tabu Learning Neurons

Sriram¹,

Njitacke

Karthikeyan

et al. 2022

Electronics

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Understanding neuron function may aid in determining the complex collective behavior of brain systems. To delineate the collective behavior of the neural network, we consider modified tabu learning neurons (MTLN) with magnetic flux. Primarily, we explore the rest points and stability of the isolated MTLN, as well as its dynamical characteristics using maximal Lyapunov exponents. Surprisingly, we discover that for a given set of parameter values with distinct initial conditions, the periodic and the chaotic attractors may coexist. In addition, experimental analysis is carried out using a microcontroller-based implementation technique to support the observed complex behavior of the MTLN. We demonstrate that the observed numerical results are in good agreement with the experimental verification. Eventually, the collective behaviors of the considered MTLN are investigated by extending them to the network of the lattice array. We discover that when the magnetic flux coupling coefficient is varied in the presence of an external stimulus, the transition from spiral waves to traveling plane waves occurs. Finally, we manifest the formation of spiral waves in the absence of an external stimulus in contrast to previous observations.

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