Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation

Asit Saha and Amiya Das ()
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Asit Saha: Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim 737136, India
Amiya Das: Department of Mathematics, University of Kalyani, Kalyani 741235, India

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 04, 1-11

Abstract: Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the first time in the literature. Bifurcation of phase portraits of the unperturbed GNWS equation is dispensed using phase plane analysis through symbolic computation and it shows stable oscillation of the traveling waves. Chaotic behavior of the perturbed GNWS equation is obtained by applying different computational tools, like phase plot, time series plot, Poincare section, bifurcation diagram and Lyapunov exponent. A period-doubling bifurcation behavior to chaotic behavior is shown for the perturbed GNWS equation and again it shows chaotic to periodic motion through inverse period-doubling bifurcation. The perturbed GNWS equation also shows chaotic motion through a sequence of periodic motions (period-1, period-3 and period-5) depending on the variation of the parameter of linear coefficient. Thus, the parameter of linear coefficient plays the role of a controlling parameter in the chaotic dynamics of the perturbed GNWS equation.

Keywords: Bifurcation; chaotic behavior; phase plot; poincaré section (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S012918312050059X

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