Some new soliton-like and doubly periodic-like solutions of Fisher equation with time-dependent coefficients

The nonlinear dynamics of a discretized form of quasi-periodic plasma perturbations model (Q-PPP) with nonlocal fractional differential operator possessing singular kernel are investigated. For example, the conditions for the stability and occurrence of Neimark–Sacker (NS) and flip bifurcations in the proposed discretized equations are provided. Moreover, analysis of nonlinearities such as the existence of chaos in this map is proved numerically via bifurcation diagrams, Lyapunov exponents and analytically via Marotto’s Theorem. Also, some simulation results are utilized to confirm the theoretical results and to show that the obtained map exhibits double routes to chaos: one is via flip bifurcation and the other is via NS bifurcation. Furthermore, more complex dynamical phenomena such as existence of closed invariant curves, homoclinic orbits, homoclinic connections, period 3 and period 4 attractors are shown. This kind of research is useful for physicists who work with tokamak models.

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Some new soliton-like and doubly periodic-like solutions of Fisher equation with time-dependent coefficients

Abstract: In this paper, the group classification is presented for Fisher equation with time-dependent coefficients. The analysis provided many new solutions that take the form of doubly periodic-like solutions and soliton-like solutions.

Cited by 7 publications

References 23 publications

Analytical Solutions for Nonlinear Fractional Physical Problems Via Natural Homotopy Perturbation Method

Analytical Solutions for Nonlinear Fractional Physical Problems Via Natural Homotopy Perturbation Method

Complex dynamics and control of a novel physical model using nonlocal fractional differential operator with singular kernel

Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations

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