Results 181 to 190 of about 10,996,377 (201)

On Melnikov's method in the study of chaotic motions of gyrostat

International Journal of Control, 2002
The homoclinic solutions of the attitude motion of a gyrostat with wheels along its principal axes are formulated using the procedure developed by Wittenburg. The generic Melnikov function for the attitude motion of a gyrostat subject to small non-linear damping torques and small periodic torques is derived.
Jinlu Kuang, Soonhie Tan, A. Y. T. Leung
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Melnikov-Type Method for a Class of Discontinuous Planar Systems and Applications

International Journal of Bifurcation and Chaos, 2014
In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed piecewise smooth planar system. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise smooth homoclinic solution transversally crossing the switching manifold.
Shuangbao Li, Wei Zhang 0084, Yuxin Hao
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Melnikov’s method for nonperiodic perturbations and the bifurcations in a Josephson junction

Physical Review B, 1987
We consider a Josephson junction with an applied dc current and nonperiodic time-dependent magnetic field. Despite this nonperiodicity, one may use Melnikov's method to derive the bifurcation curves analytically. We give the critical theoretical value I/sub c/ of the dc current separating qualitatively different regions, essentially one region where ...
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The Multiple Scales Method, Homoclinic Bifurcation and Melnikov's Method for Autonomous Systems

International Journal of Bifurcation and Chaos, 1998
Melnikov's method is a well-established technique for detecting homoclinic bifurcation of perturbed autonomous or forced systems. This method uses a regular perturbation expansion in terms of a small parameter in the system. Whilst the approach correctly estimates the parameter values for the bifurcation and transverse intersections of separatrices ...
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Using Melnikov's method to solve Silnikov's problems

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1990
SynopsisA function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite.
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Application of Melnikov's Method to the Reduced KdV Equation

Australian Journal of Physics, 1991
The Melnikov method for estimating distances between invariant manifolds is applied to the perturbed system of ordinary differential equations obtained from the KdV equation, reduced by a travelling wave ansatz and including a diffusion term. The calculation is performed after one integration and the result is compared with numerical work carried out ...
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Melnikov-type method for chaos in a class of hybrid piecewise-smooth systems with impact and noise excitation under unilateral rigid constraint

Applied Mathematical Modelling, 2023
Zhouchao Wei, Tomasz Kapitaniak
exaly  

Application of the extended Melnikov's method for single-degree-of-freedom vessel roll motion

Ocean Engineering, 2008
Wan Wu, Leigh McCue
exaly  

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations

Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2006
Ricardo Chacon
exaly  

Melnikov method and detection of chaos for non-smooth systems

Acta Mathematicae Applicatae Sinica, 2013
Tassilo Kupper
exaly