Dynamics of a ring of three fractional-order Duffing oscillators

Living-Neuron-Based Autogenerator

“…Breakthroughs in control theory and nonlinear dynamics have driven the evolution of mathematical theories and physical models of neurons as dynamical systems, from individual elements [1][2][3] to complex neural networks [4,5]. Synchronization processes have played a crucial role in encoding and decoding neural dynamics, revealing the importance of self-organization processes in neuronal dynamics [6][7][8][9]. Furthermore, it has been demonstrated over time that the foundation of neuronal dynamics lies in the self-organization process of complex systems [10,11].…”

Caputo-Hadamard fractional chaotic maps

“…Many models with difference types of fractional derivatives has been proposed to describe different problems with various background. It is found that the fractional model can give a description of some properties and phenomena of objects more accurately than the integer model, such as the memory and genetic properties of different substances and processes [1,2], anomalous diffusion problem [3], modeling hydraulics [4] and circuit networks [5], applications in finance [6], sociology [7], infectious disease [8][9][10], physics [11,12], quantum mechanics [13,14], optics [15], chaos dynamics [16], chemistry, engineering [4], viscoelasticity, rheology, neural networks [5,[17][18][19], fractal and chaos [20] and many other fields.…”

“…Wu and other scholars studied the stability of variable fractional-order Chen chaotic system, fractional-order Hénon map, variable fractional order logistic map and short memory equation [34][35][36]. The dynamic analysis of other fractional systems has been done, such as fractional-order Ikeda map [37], the discrete fractional duffing system [38], fractional-order hyperchaotic complex system [39], fractional-order laser hyperchaotic system [40], three fractional-order Duffing oscillators [11], fractional-order six-order discrete chaotic mapping, fractional quadric polynomial map and fractional quantum logistic map [14,41,42].…”

Dynamic analysis of new two‐dimensional fractional‐order discrete chaotic map and its application in cryptosystem

“…Fiaz et al studied the generalization of synchronization of three‐dimensional fractional chaotic systems 14 . Barba‐Franco et al studied the dynamical behavior of a system consisting of three fractional Duffing oscillators coupled together 15 . The fractional Fokker–Planck equation on fractal media is derived together with the continuous time random walk 13 …”