The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations

Dec 25, 2023

Journal Tikrit Journal of Pure Science

publisher Tikrit University

DOI https://doi.org/10.25130/tjps.v28i6.1382

Issue 6

Volume 28

This study focuses on the stability and catastrophic behavior of finite periodic solutions in non-linear differential equations. The occurrence of folding surfaces and their relationship with saddle-node bifurcations are explored, being classified as fold and butterfly types of catastrophes. Additionally, the application of catastrophe theory is discussed to analyze the qualitative changes in solutions with the change in system parameters.

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On the Butterfly Catastrophe Model and Stability of Finite Periodic Solutions for Some Non-Linear Differential Equations

Mar 31, 2023

Journal Journal- Scientific Studies

publisher Kirkuk University

DOI doi:10.32894/kujss.2023.136973.1089

Issue 1

Volume 18

In this work, we find the results for the folded part projection of the butterfly catastrophe model onto the control space, using methods from catastrophe theory to obtain stability and the catastrophic behavior of finite periodic solutions for some non-linear differential equations. Finally, we have shown that a saddle-node bifurcation, which can be classified as a butterfly mutation, accompanies butterfly surface folding.

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