Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing

Abstract

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.

Chaotic Motion of Double-walled Carbon Nanotubes with Fluid

“…(2)(3)(4)(5) Recently, many researchers have been studying the characteristics of nanotube vibration, (6)(7)(8)(9) and have investigated, among others, nonlinear vibration problems with nonlocal continuum theories. (10)(11)(12)(13)(14)(15) In the past, much research has been reported on the chaotic behaviors of nonlinear systems; (16)(17)(18)(19) however, investigations about the chaotic behavior of double-walled carbon nanotubes (DWCNTs) with fluid are rare. The chaotic motion is primarily generated thanks to the nonlinear characteristics in the physical system.…”

Chaotic Motion in Forced Duffing System Subject to Linear and Nonlinear Damping

“…However, the consideration of nonlinear damping is quite necessary in various engineering applications such as drag forces in flow induced vibrations [4] and vibration isolators [11]. Among others, some researches have made the contributions to the chaotic behavior of Duffing oscillator due to nonlinear damping [12][13][14][15][16][17][18][19][20][21].…”

Dynamical behaviour of parametrically driven Duffing and externally driven Helmholtz–Duffing oscillators under nonlinear dissipation

“…It also plays a very important role in deciding the boarder of stability and instability of physical systems. There have been several efforts recently to understand the effect of nonlinear damping on the dynamical behaviour of some of the ubiquitous physical oscillators like forced Duffing, escape oscillator, Rayleigh-Duffing Oscillator and forced pendulum [1][2][3][4][5][6][7][8][9][10][11]. The main focus of the present work is to study the effect of nonlinear damping on the overall dynamical behaviour of the two important versions of Duffing oscillator, i.e.…”

“…They completely described the topology in various regions of the parameter plane and are associated with variations in system parameters. In 2009, Litak et al [7] considered parametric forcing in the self-excited system with a cubic double-well potential. In this work, they examined the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double-well nonlinear potential.…”