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Papers by durval tonon

Research paper thumbnail of Piecewise smooth reversible dynamical systems at a two-fold singularity

arXiv (Cornell University), Nov 21, 2011

This paper treats on the existence of closed orbits around a two-fold singularity of 3D discontin... more This paper treats on the existence of closed orbits around a two-fold singularity of 3D discontinuous systems of the Filippov type in presence of symmetries.

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Research paper thumbnail of Phippov systems in tridimensional manifolds

Orientador: Marco Antonio TeixeiraTese (doutorado) - Universidade Estadual de Campinas, Instituto... more Orientador: Marco Antonio TeixeiraTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Neste trabalho sistemas dinâmicos descontínuos em variedades tridimensionais são estudados. Descrevemos uma classe de tais sistemas que são localmente estruturalmente estáveis em uma vizinhança de uma singularidade típica. Exibimos nessa etapa uma sub-família de campos do tipo dobra-dobra que é estruturalmente estável. Introduzimos os conceitos de A e L-estabilidade, que são pequenas generalizações dos conceitos clássicos de estabilidade assintótica e estabilidade no sentido de Lyapunov, respectivamente. Através de formas normais para as famílias de campos descontínuos de codimensão zero e um, exibimos os subconjuntos de sistemas descontínuos que são A e L-estáveis em uma vizinhança da origem. Destacamos um dos principais objetos de estudo desse trabalho: a singularidade dobra-dobra caso elíptico (T-singularidade). Discutimos alg...

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Research paper thumbnail of An asymptotically stable cusp-fold singularity in 3D piecewise smooth vector fields

arXiv (Cornell University), Jun 6, 2013

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Research paper thumbnail of The chaotic behaviour of piecewise smooth differential equations on two-dimensional torus and sphere

Dynamical Systems-an International Journal, Nov 2, 2018

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Research paper thumbnail of Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator

Nonlinearity, Jun 22, 2022

In this paper a generalised Rayleigh–Liénard oscillator is consider and lower bounds for the numb... more In this paper a generalised Rayleigh–Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. More precisely, the approach consists in perform suitable changes in the sign of some specific parameters and apply Poincaré–Bendixson theorem for assure the existence of limit cycles. In particular, the algorithm for obtaining the limit cycles through the referred approach is explicitly exhibited. The main techniques applied in this study are the Lyapunov constants and the Melnikov method. The obtained results contemplate the simultaneity of limit cycles of small amplitude and medium amplitude, the former emerging from a weak focus equilibrium and the latter from homoclinic or heteroclinic saddle connections.

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Research paper thumbnail of Symmetric periodic orbits for the collinear charged 3-body problem

Journal of Mathematical Physics, Feb 1, 2017

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Research paper thumbnail of Limit cycles of discontinuous piecewise polynomial vector fields

Journal of Mathematical Analysis and Applications, May 1, 2017

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Research paper thumbnail of Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields

International Journal of Bifurcation and Chaos, Jul 1, 2014

In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a sce... more In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a scenario, the main goal of this paper is to exhibit the homeomorphism that gives the topological equivalence between a codimension one piecewise smooth vector field and the respective C0-normal form.

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Research paper thumbnail of Piecewise Smooth Reversible Dynamical Systems at a Two-Fold Singularity

International Journal of Bifurcation and Chaos, Aug 1, 2012

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Research paper thumbnail of Global Analysis of the Dynamics of a Piecewise Linear Vector Field Model for Prostate Cancer Treatment

Journal of Dynamical and Control Systems, Oct 29, 2021

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Research paper thumbnail of Asymptotic Stability in Some Generic Classes of Three-Dimensional Discontinuous Dynamical Systems

RSME Springer series, 2020

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Research paper thumbnail of The symmetric periodic orbits for the two-electron atom

Letters in Mathematical Physics, Feb 5, 2018

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Research paper thumbnail of Detecting periodic orbits in some 3D chaotic quadratic polynomial differential systems

Discrete and Continuous Dynamical Systems-series B, Nov 1, 2015

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Research paper thumbnail of Crossing Periodic Orbits via First Integrals

International Journal of Bifurcation and Chaos, Sep 15, 2020

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Research paper thumbnail of Sliding motion on tangential sets of Filippov systems

arXiv (Cornell University), Nov 24, 2021

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Research paper thumbnail of Lower bounds for the number of limit cycles in a generalized Rayleigh-Li\'enard oscillator

arXiv (Cornell University), Dec 27, 2020

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Research paper thumbnail of Bifurcations of Non Smooth Vector Fields on <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\R^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> by Geometric Singular Perturbations

arXiv (Cornell University), Nov 21, 2011

Our object of study is non smooth vector fields on R2\R^2R2. We apply the techniques of geometric s... more Our object of study is non smooth vector fields on R2\R^2R2. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way we are able to bring out some results that bridge the space between non$-$smooth dynamical systems presenting typical singularities and singularly perturbed smooth systems.

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Research paper thumbnail of Two-fold symmetric singularity

arXiv (Cornell University), Nov 21, 2011

We explore some qualitative dynamics in the neighborhood of the 3−dimensional3-dimensional3−dimensional two-fold symmetri... more We explore some qualitative dynamics in the neighborhood of the 3−dimensional3-dimensional3−dimensional two-fold symmetric singularity. We study the existence of an one-parameter family of regular (pseudo) periodic orbits of such systems near a reversible two-fold singularity.

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Research paper thumbnail of Chaos in Piecewise Smooth Vector Fields on Two Dimensional Torus and Sphere

arXiv (Cornell University), Jan 21, 2016

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Research paper thumbnail of Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si58.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:m...

Physica D: Nonlinear Phenomena, May 1, 2017

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Research paper thumbnail of Piecewise smooth reversible dynamical systems at a two-fold singularity

arXiv (Cornell University), Nov 21, 2011

This paper treats on the existence of closed orbits around a two-fold singularity of 3D discontin... more This paper treats on the existence of closed orbits around a two-fold singularity of 3D discontinuous systems of the Filippov type in presence of symmetries.

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Research paper thumbnail of Phippov systems in tridimensional manifolds

Orientador: Marco Antonio TeixeiraTese (doutorado) - Universidade Estadual de Campinas, Instituto... more Orientador: Marco Antonio TeixeiraTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Neste trabalho sistemas dinâmicos descontínuos em variedades tridimensionais são estudados. Descrevemos uma classe de tais sistemas que são localmente estruturalmente estáveis em uma vizinhança de uma singularidade típica. Exibimos nessa etapa uma sub-família de campos do tipo dobra-dobra que é estruturalmente estável. Introduzimos os conceitos de A e L-estabilidade, que são pequenas generalizações dos conceitos clássicos de estabilidade assintótica e estabilidade no sentido de Lyapunov, respectivamente. Através de formas normais para as famílias de campos descontínuos de codimensão zero e um, exibimos os subconjuntos de sistemas descontínuos que são A e L-estáveis em uma vizinhança da origem. Destacamos um dos principais objetos de estudo desse trabalho: a singularidade dobra-dobra caso elíptico (T-singularidade). Discutimos alg...

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Research paper thumbnail of An asymptotically stable cusp-fold singularity in 3D piecewise smooth vector fields

arXiv (Cornell University), Jun 6, 2013

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Research paper thumbnail of The chaotic behaviour of piecewise smooth differential equations on two-dimensional torus and sphere

Dynamical Systems-an International Journal, Nov 2, 2018

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Research paper thumbnail of Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator

Nonlinearity, Jun 22, 2022

In this paper a generalised Rayleigh–Liénard oscillator is consider and lower bounds for the numb... more In this paper a generalised Rayleigh–Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. More precisely, the approach consists in perform suitable changes in the sign of some specific parameters and apply Poincaré–Bendixson theorem for assure the existence of limit cycles. In particular, the algorithm for obtaining the limit cycles through the referred approach is explicitly exhibited. The main techniques applied in this study are the Lyapunov constants and the Melnikov method. The obtained results contemplate the simultaneity of limit cycles of small amplitude and medium amplitude, the former emerging from a weak focus equilibrium and the latter from homoclinic or heteroclinic saddle connections.

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Research paper thumbnail of Symmetric periodic orbits for the collinear charged 3-body problem

Journal of Mathematical Physics, Feb 1, 2017

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Research paper thumbnail of Limit cycles of discontinuous piecewise polynomial vector fields

Journal of Mathematical Analysis and Applications, May 1, 2017

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Research paper thumbnail of Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields

International Journal of Bifurcation and Chaos, Jul 1, 2014

In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a sce... more In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a scenario, the main goal of this paper is to exhibit the homeomorphism that gives the topological equivalence between a codimension one piecewise smooth vector field and the respective C0-normal form.

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Research paper thumbnail of Piecewise Smooth Reversible Dynamical Systems at a Two-Fold Singularity

International Journal of Bifurcation and Chaos, Aug 1, 2012

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Research paper thumbnail of Global Analysis of the Dynamics of a Piecewise Linear Vector Field Model for Prostate Cancer Treatment

Journal of Dynamical and Control Systems, Oct 29, 2021

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Research paper thumbnail of Asymptotic Stability in Some Generic Classes of Three-Dimensional Discontinuous Dynamical Systems

RSME Springer series, 2020

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Research paper thumbnail of The symmetric periodic orbits for the two-electron atom

Letters in Mathematical Physics, Feb 5, 2018

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Research paper thumbnail of Detecting periodic orbits in some 3D chaotic quadratic polynomial differential systems

Discrete and Continuous Dynamical Systems-series B, Nov 1, 2015

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Research paper thumbnail of Crossing Periodic Orbits via First Integrals

International Journal of Bifurcation and Chaos, Sep 15, 2020

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Research paper thumbnail of Sliding motion on tangential sets of Filippov systems

arXiv (Cornell University), Nov 24, 2021

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Research paper thumbnail of Lower bounds for the number of limit cycles in a generalized Rayleigh-Li\'enard oscillator

arXiv (Cornell University), Dec 27, 2020

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Research paper thumbnail of Bifurcations of Non Smooth Vector Fields on <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\R^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> by Geometric Singular Perturbations

arXiv (Cornell University), Nov 21, 2011

Our object of study is non smooth vector fields on R2\R^2R2. We apply the techniques of geometric s... more Our object of study is non smooth vector fields on R2\R^2R2. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way we are able to bring out some results that bridge the space between non$-$smooth dynamical systems presenting typical singularities and singularly perturbed smooth systems.

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Research paper thumbnail of Two-fold symmetric singularity

arXiv (Cornell University), Nov 21, 2011

We explore some qualitative dynamics in the neighborhood of the 3−dimensional3-dimensional3−dimensional two-fold symmetri... more We explore some qualitative dynamics in the neighborhood of the 3−dimensional3-dimensional3−dimensional two-fold symmetric singularity. We study the existence of an one-parameter family of regular (pseudo) periodic orbits of such systems near a reversible two-fold singularity.

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Research paper thumbnail of Chaos in Piecewise Smooth Vector Fields on Two Dimensional Torus and Sphere

arXiv (Cornell University), Jan 21, 2016

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Research paper thumbnail of Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si58.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:m...

Physica D: Nonlinear Phenomena, May 1, 2017

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