Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator
Joint Authors
Fangnon, R.
Ainamon, C.
Monwanou, A. V.
Miwadinou, C. H.
Chabi Orou, J. B.
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-09
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
In this paper, the Helmholtz equation with quadratic damping themes is used for modeling the dynamics of a simple prey-predator system also called a simple Lotka–Volterra system.
From the Helmholtz equation with quadratic damping themes obtained after modeling, the equilibrium points have been found, and their stability has been analyzed.
Subsequently, the harmonic oscillations have been studied by the harmonic balance method, and the phenomena of resonance and hysteresis are observed.
The primary and secondary resonances have been researched by the multiple-scale method, and the conditions of stability of the amplitudes of oscillations are determined.
Chaos is detected analytically by the Melnikov method and numerically using the basin of attraction, the bifurcation diagram, the Lyapunov exponent, the phase portrait, and the Poincaré section.
The effects of all the parameters of the system are analyzed in detail, and special emphasis is placed on the new parameters.
Through this analysis, the complex phenomena such as hysteresis, bistability, amplitude jump, resonances, and chaos have been obtained.
The control of the parameters and the necessary conditions to control the aforementioned phenomena have been found.
American Psychological Association (APA)
Fangnon, R.& Ainamon, C.& Monwanou, A. V.& Miwadinou, C. H.& Chabi Orou, J. B.. 2020. Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator. Complexity،Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1144691
Modern Language Association (MLA)
Fangnon, R.…[et al.]. Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator. Complexity No. 2020 (2020), pp.1-17.
https://search.emarefa.net/detail/BIM-1144691
American Medical Association (AMA)
Fangnon, R.& Ainamon, C.& Monwanou, A. V.& Miwadinou, C. H.& Chabi Orou, J. B.. Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator. Complexity. 2020. Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1144691
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1144691