The Experts below are selected from a list of 93 Experts worldwide ranked by ideXlab platform
A M Alves - One of the best experts on this subject based on the ideXlab platform.
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bifurcation of limit cycles by perturbing piecewise non hamiltonian systems with nonlinear Switching Manifold
Nonlinear Analysis-real World Applications, 2021Co-Authors: O Ramirez, A M AlvesAbstract:Abstract This paper is devoted to the study of limit cycles that can bifurcate of a perturbation of piecewise non-Hamiltonian systems with nonlinear Switching Manifold. We derive the first order Melnikov function to these systems. As application, the sharp upper bound of the number of bifurcated limit cycles of two concrete systems, whose Switching Manifolds are algebraic curves, is presented.
O Ramirez - One of the best experts on this subject based on the ideXlab platform.
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bifurcation of limit cycles by perturbing piecewise non hamiltonian systems with nonlinear Switching Manifold
Nonlinear Analysis-real World Applications, 2021Co-Authors: O Ramirez, A M AlvesAbstract:Abstract This paper is devoted to the study of limit cycles that can bifurcate of a perturbation of piecewise non-Hamiltonian systems with nonlinear Switching Manifold. We derive the first order Melnikov function to these systems. As application, the sharp upper bound of the number of bifurcated limit cycles of two concrete systems, whose Switching Manifolds are algebraic curves, is presented.
Novaes, Douglas D. - One of the best experts on this subject based on the ideXlab platform.
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Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear Switching curve
2020Co-Authors: Andrade, Kamila Da S., Cespedes, Oscar A. R., Cruz, Dayane R., Novaes, Douglas D.Abstract:In this paper, we are interested in providing lower estimations for the maximum number of limit cycles $H(n)$ that planar piecewise linear differential systems with two zones separated by the curve $y=x^n$ can have, where $n$ is a positive integer. For this, we perform a higher order Melnikov analysis for piecewise linear perturbations of the linear center. In particular, we obtain that $H(2)\geq 4,$ $H(3)\geq 8,$ $H(n)\geq7,$ for $n\geq 4$ even, and $H(n)\geq 9,$ for $n\geq 5$ odd. This improves all the previous results for $n\geq2.$ Our analysis is mainly based on some recent results about Chebyshev systems with positive accuracy and Melnikov Theory, which will be developed at any order for a class of nonsmooth differential systems with nonlinear Switching Manifold
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Melnikov analysis in nonsmooth differential systems with nonlinear Switching Manifold
Estados Unidos, 2020Co-Authors: Bastos, Jéfferson L. R., Llibre Jaume, Buzzi, Claudio A., Novaes, Douglas D.Abstract:We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the Switching Manifold is added to the second order averaged function267637483767CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQCOORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPESFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP306649/2018-7; 438975/2018-988881.068462/2014-012013/24541-0; 2016/11471-2; 2018/16430-8Brazilian FAPESP grant [2013/24541-0, 2016/11471-2, 2018/16430-8]; Brazilian CapesCAPES [88881.068462/2014-01]; FEDER-MINECO grant [MTM2016-77278-P]; MINECO grant [MTM2013-40998-P]; AGAUR grantAgencia de Gestio D'Ajuts Universitaris de Recerca Agaur (AGAUR) [2014SGR-568]; Brazilian CNPqNational Council for Scientific and Technological Development (CNPq) [306649/2018-7, 438975/2018-9
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Melnikov analysis in nonsmooth differential systems with nonlinear Switching Manifold
'Elsevier BV', 2019Co-Authors: Bastos, Jéfferson L. R., Buzzi Claudio, Llibre Jaume, Novaes, Douglas D.Abstract:We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the Switching Manifold is added to the second order averaged function
Yuxin Hao - One of the best experts on this subject based on the ideXlab platform.
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the melnikov method for detecting chaotic dynamics in a planar hybrid piecewise smooth system with a Switching Manifold
Nonlinear Dynamics, 2017Co-Authors: Xiaojun Gong, Wei Zhang, Yuxin HaoAbstract:In this paper, we extend the classical Melnikov method for smooth systems to a class of planar hybrid piecewise-smooth system subjected to a time-periodic perturbation. In this class, we suppose there exists a Switching Manifold with a more general form such that the plane is divided into two zones, and the dynamics in each zone is governed by a smooth system. Furthermore, we assume that the unperturbed system is a general planar piecewise-smooth system with non-zero trace and possesses a piecewise-smooth homoclinic orbit transversally crossing the Switching Manifold. We also define a reset map to describe the instantaneous impact rule on the Switching Manifold when a trajectory arrives at the Switching Manifold. Through a series of geometrical analysis and perturbation techniques, we obtain a Melnikov-type function to measure the separation of the unstable Manifold and stable Manifold under the effect of the time-periodic perturbations and the reset map. Finally, we use the presented Melnikov function to study global bifurcations and chaotic dynamics for a concrete planar piecewise-linear oscillator.
Xiaojun Gong - One of the best experts on this subject based on the ideXlab platform.
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the melnikov method for detecting chaotic dynamics in a planar hybrid piecewise smooth system with a Switching Manifold
Nonlinear Dynamics, 2017Co-Authors: Xiaojun Gong, Wei Zhang, Yuxin HaoAbstract:In this paper, we extend the classical Melnikov method for smooth systems to a class of planar hybrid piecewise-smooth system subjected to a time-periodic perturbation. In this class, we suppose there exists a Switching Manifold with a more general form such that the plane is divided into two zones, and the dynamics in each zone is governed by a smooth system. Furthermore, we assume that the unperturbed system is a general planar piecewise-smooth system with non-zero trace and possesses a piecewise-smooth homoclinic orbit transversally crossing the Switching Manifold. We also define a reset map to describe the instantaneous impact rule on the Switching Manifold when a trajectory arrives at the Switching Manifold. Through a series of geometrical analysis and perturbation techniques, we obtain a Melnikov-type function to measure the separation of the unstable Manifold and stable Manifold under the effect of the time-periodic perturbations and the reset map. Finally, we use the presented Melnikov function to study global bifurcations and chaotic dynamics for a concrete planar piecewise-linear oscillator.
