Amplitude response, Melnikov's criteria, and chaos occurrence in a Duffing's system subjected to an external periodic excitation with a variable shape.

Autor:	Ndjomatchoua FT; Spatial Transformation of Landscapes, Sustainable Impact through Rice-Based Systems, International Rice Research Institute (IRRI), DAPO Box 7777-1301, Metro Manila, Philippines., Djomo TLM; Department of Civil Engineering, National Higher Polytechnic Institute, University of Bamenda, P.O. BOX 39, Bambili, Bamenda, Cameroon., Kemwoue FF; Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon., Gninzanlong CL; Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon., Kepnang MP; Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon., Siewe MS; Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon., Tchawoua C; Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon., Pedro SA; Departamento de Matemática e Informatica, Faculdade de Ciências, Universidade Eduardo Mondlane, 254 Maputo, Mozambique., Kofane TC; Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon.
Jazyk:	angličtina
Zdroj:	Chaos (Woodbury, N.Y.) [Chaos] 2022 Aug; Vol. 32 (8), pp. 083144.
DOI:	10.1063/5.0082235
Abstrakt:	The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach. Interestingly, the frequency-response curve displays a large number of resonance peaks and anti-resonance peaks as well. Surprisingly, a resonance phenomenon termed here as shape-induced-resonance is noticed as it occurs solely due to the change in the shape parameter of the external periodic force. The system exhibits amplitude jumps and hysteresis depending on r. The critical driving magnitude for the chaos occurrence is investigated through Melnikov's method. Numerical analysis based on bifurcation diagrams and Lyapunov exponent is used to show how chaos occurs in the system. It is shown that the threshold amplitude of the excitation to observe chaotic dynamics decreases/increases for small/large values of r. In general, the theoretical estimates match with numerical simulations and electronic simulations as well.
Databáze:	MEDLINE
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