scholarly journals Localizing Bifurcations in Non-Linear Dynamical Systems via Analytical and Numerical Methods

Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 127
Author(s):  
Jan Kyzioł ◽  
Andrzej Okniński

In this paper, we study the bifurcations of non-linear dynamical systems. We continue to develop the analytical approach, permitting the prediction of the bifurcation of dynamics. Our approach is based on implicit (approximate) amplitude-frequency response equations of the form FΩ,A;c̲=0, where c̲ denotes the parameters. We demonstrate that tools of differential geometry make possible the discovery of the change of differential properties of solutions of the equation FΩ,A;c̲=0. Such qualitative changes of the solutions of the amplitude-frequency response equation, referred to as metamorphoses, lead to qualitative changes of dynamics (bifurcations). We show that the analytical prediction of metamorphoses is of great help in numerical simulation.

2003 ◽  
Vol 155 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Tarcı́sio M. Rocha Filho ◽  
Iram M. Gléria ◽  
Annibal Figueiredo

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