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

Complexity

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

Philosophy

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