Investigation of Bifurcations in the Process Equation

DOI10.1142/S0218127417502017zbMATH Open1381.39005arXiv1703.00419OpenAlexW2593296385MaRDI QIDQ4601768

Seyed Mohammad Reza Hashemi Golpayegani, Fahimeh Nazarimehr, Louis Kauffman, Sajad Jafari

Publication date: 24 January 2018

Published in: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering (Search for Journal in Brave)

Abstract: This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period doubling route to chaos, bios, unstable windows and periodic windows. In this note, we focus on different behaviors of the process equation by a deep look at phase portraits and cobweb plots. Therefore, period doubling route to chaos and unifurcations of the equation are investigated, and also the parameter of its entrance to biotic pattern is discussed. The control parameter for the process equation is g (the coupling constant). In higher g, the system shows some unstable and periodic windows among the biotic behaviors. Different patterns of these windows and the reasons of their happenings are investigated mathematically. In addition, some other types of unstable and periodic windows are discussed and Q-curves determine the difference of these windows with the previous ones.

Full work available at URL: https://arxiv.org/abs/1703.00419

zbMATH Keywords

bifurcationmultistablebiosbio-periodic windowprocess equationunifurcationunstable window

Mathematics Subject Classification ID

Additive difference equations (39A10) Discrete version of topics in analysis (39A12) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Numerical chaos (65P20) Dynamical aspects of attractors and their bifurcations (37G35) Numerical bifurcation problems (65P30)

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