Related papers: Transition to Chaos in the Self-Excited System wit…
We examine the Melnikov criterion for transition to chaos in case of a single degree of freedom nonlinear oscillator with the Ueda well potential and an external periodic excitation term. Using effective Hamiltonian we have examined…
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of a double well dynamical system with a nonlinear fractional damping term and external excitation. The usual double well…
We examine the Mielnikov criterion for transition to chaos in case of one degree of freedom nonlinear oscillator with non symmetric potential. This system subjected to an external periodic force shows homoclinic transition from regular…
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a…
We study the dynamics of a two-degrees-of-freedom (two DOF) nonlinear oscillator representing a quartercar model excited by a road roughness profile. Modelling the road profile by means of a harmonic function we derive the Melnikov…
A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative, oscillator systems by weak harmonic excitations is presented, including diverse applications…
The new phenomenon of semiquantum chaos is analyzed in a classically regular double-well oscillator model. Here it arises from a doubling of the number of effectively classical degrees of freedom, which are nonlinearly coupled in a Gaussian…
The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of a quarter car model excited kinematically by the road surface profile. By analyzing the potential an analytic expression is…
The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator for a specific parametric choice ($\mid \alpha \mid =\beta$) is studied. The existence of different attractors in the system parameters ($f-\omega$) domain is…
We present an experimental study of the Duffing--Holmes oscillator with a double-well potential, implemented as an analog electronic circuit under periodic external forcing. By systematically varying the forcing amplitude and frequency, we…
We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…
The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\hbar$ is increased. We show evidence to the contrary in the behavior of…
We analyze, by means of Melnikov method, the possibility of modifying the threshold of homoclinic chaos in general 1-dimensional problems, by introducing small periodic resonant modulations. We indicate in particular a prescription in order…
We consider the motion of a damped particle in a potential oscillating slowly between a simple and a double well. The system displays hysteresis effects which can be of periodic or chaotic type. We explain this behaviour by computing an…
Tunnelling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well as well as the complex dynamics under the confining barrier. These orbits…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
We study the motion of a classical particle interacting with one, two, and finally an infinite chain of 1D square wells with oscillating depth. For a single well we find complicated scattering behavior even though there is no topological…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
We study and characterize a direct route to high-dimensional chaos (i.e. not implying an intermediate low-dimensional attractor) of a system composed out of three coupled Lorenz oscillators. A geometric analysis of this medium-dimensional…
This paper considers effect of nonlinear dissipation on the basin boundaries of a driven two-well Modified Rayleigh-Duffing Oscillator where pure and unpure quadratic and cubic nonlinearities are considered. By analyzing the potential, an…