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Artículos, Encontrados 11 registros
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Artículos Encontrados 11 registros  1 - 10siguiente  ir al registro:
1.
7 p, 3.9 MB Zero-Hopf bifurcation in the Chua's circuit / Ginoux, Jean-Marc (Université de Toulon. Laboratoire LSIS) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
An equilibrium point of a differential system in R 3 such that the eigenvalues of the Jacobian matrix of the system at the equilibrium are 0 and ±ωi with ω > 0 is called a zero-Hopf equilibrium point. [...]
2023 - 10.1063/5.0137020
Journal of Mathematical Physics, Vol. 64, Issue 7 (July 2023) , art. 72701  
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2.
A family of periodic orbits for the extended Hamiltonian system of the Van der Pol oscillator / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we show a new way of using the averaging theory for studying families of periodic orbits of a Hamiltonian system. We do this study computing a new family of periodic orbits of the extension of the Van der Pol oscillator to a Hamiltonian system of two degrees of freedom.
2023 - 10.1016/j.geomphys.2022.104705
Journal of geometry and physics, Vol. 183 (January 2023) , art. 104705  
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3.
Flow curvature manifold and energy of generalized Liénard systems / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon) ; Lebiedz, Dirk (Ulm University. Institute of Numerical Mathematics) ; Meucci, Riccardo (Istituto Nazionale di Ottica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In his famous book entitled Theory of Oscillations, Nicolas Minorsky wrote: "each time the system absorbs energy the curvature of its trajectory decreases and vice versa". By using the Flow Curvature Method, we establish that, in the ε-vicinity of the slow invariant manifold of generalized Liénard systems, the curvature of trajectory curve increases while the energy of such systems decreases. [...]
2022 - 10.1016/j.chaos.2022.112354
Chaos, solitons and fractals, Vol. 161 (August 2022) , art. 112354  
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4.
11 p, 569.3 KB Rocard's 1941 chaotic relaxation econometric oscillator / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon) ; Jovanovic, Franck (Teluq University. Université d'Orléans. School of Business Administration) ; Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In the beginning of the Second World War, the French physicist, Yves Rocard, published a book entitled Théorie des Oscillateurs (Theory of Oscillators). In Chapter V, he designed a mathematical model consisting of a set of three nonlinear differential equations and allowing to account for economic cycles. [...]
2022 - 10.1142/S0218127422500432
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 3 (March 2022) , art. 2250043  
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5.
17 p, 655.4 KB Dynamics and Darboux integrability of the D 2 polynomial vector fields of degree 2 in ℝ3 / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon. Centre de Physique Théorique (France)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We characterize the Darboux integrability and the global dynamics of the 3-dimensional polynomial differential systems of degree 2 which are invariant under the D2 symmetric group, which have been partially studied previously by several authors.
2021 - 10.1007/s11040-020-09372-0
Mathematical Physics, Analysis and Geometry, Vol. 24, Issue 1 (March 2021) , art. 1  
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6.
9 p, 632.0 KB Zero-hopf bifurcation in the volterra-gause system of predator-prey type / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique (França)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. [...]
2017 - 10.1002/mma.4569
Mathematical methods in the applied sciences, Vol. 40, Issue 18 (December 2017) , p. 7858-7866  
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7.
16 p, 706.1 KB Canards existence in the Hindmarsh-Rose model / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique (França)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tchizawa, Kiyoyuki (Institute of Administration Engineering Ltd. (Japan))
In two previous papers we have proposed a new method for proving the existence of "canard solutions" on one hand for three and four-dimensional singularly perturbed systems with only one fast variable and, on the other hand for four-dimensional singularly perturbed systems with two fast variables [J. [...]
2019 - 10.1051/mmnp/2019012
Mathematical Modelling of Natural Phenomena, Vol. 14, Issue 4 (2019) , art. 409
2 documentos
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8.
46 p, 1.1 MB Canards Existence in Memristor's Circuits / Ginoux, Jean-Marc (Université de Toulon(France). Laboratoire LSIS) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The aim of this work is to propose an alternative method for determining the condition of existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable in the folded saddle case. [...]
2016 - 10.1007/s12346-015-0160-1
Qualitative theory of dynamical systems, 2016  
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9.
38 p, 1.1 MB Canards existence in FitzHugh-Nagumo and Hodgkin-Huxley neuronal models / Ginoux, Jean-Marc (Université de Toulon(France). Laboratoire LSIS) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In a previous paper we have proposed a new method for proving the existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable. The aim of this work is to extend this method to the case of four-dimensional singularly perturbed systems with two slow and two fast variables. [...]
2015 - 10.1155/2015/342010
Mathematical Problems in Engineering, Vol. 2015 art. 342010, p. 17pp.  
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10.
21 p, 917.4 KB Canards from Chua's circuit / Ginoux, Jean-Marc (Université du Sud(France). Laboratoire Protee) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Chua, Leon O. (University of California. DEECS Department)
At first, the aim of this work is to extend Benoît's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. [...]
2013 - 10.1142/S0218127413300103
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 4 (2013) , p. 1330010  
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Artículos : Encontrados 11 registros   1 - 10siguiente  ir al registro:
Libros y colecciones Encontrados 1 registros  
1.
5 p, 251.1 KB Canards existence in the Hindmarsh-Rose model / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique (França)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tchizawa, Kiyoyuki (Institute of Administration Engineering Ltd. (Japan))
In two previous papers, we have proposed a new method for proving the existence of "canard solutions" on one hand for three- and four-dimensional singularly perturbed systems with only one fast variable and, on the other hand, for four-dimensional singularly perturbed systems with two fast variables; see [4, 5]. [...]
Cham, etc : Birkhäuser, cop. 2019 (Trends in mathematics. Research perspectives CRM Barcelona ; 11) - 10.1007/978-3-030-25261-8_26
Extended abstracts Spring 2018 : singularly perturbed systems, multiscale phenomena and hysteresis: theory and applications, 2019, p. 169-175  
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