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| Pàgina inicial > Articles > Articles publicats > A new result on averaging theory for a class of discontinuous planar differential systems with applications |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade Estadual de Campinas. Departamento de Matemática (Brazil))| Data: | 2017 |
| Resum: | We develop the averaging theory at any order for computing the periodic solutions of periodic discontinuous piecewise differential system of the form dr/dθ= r'={F+(θ, r, ϵ) if 0≤ θ ≤ α, F-(θ, r, ϵ) if α ≤ θ ≤ 2π, where F±(θ, r, ϵ) = Σk i=1 ϵiF± i (θ, r) + ϵk+1R ± (θ, r, ϵ) with θ ϵ S and r ϵ D, where D is an open interval of ℝ+, and ϵ is a small real parameter. Applying this theory, we provide lower bounds for the maximum number of limit cycles that bifurcate from the origin of quartic polynomial differential systems of the form x = -y+xp(x, y), y = x+yp(x, y), with p(x, y) a polynomial of degree 3 without constant term, when they are perturbed, either inside the class of all continuous quartic polynomial differential systems, or inside the class of all discontinuous piecewise quartic polynomial differential systems with two zones separated by the straight line y = 0. |
| Ajuts: | Ministerio de Economía y Competitividad MTM2009-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 |
| Nota: | Altres ajuts: ICREA Academia |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Periodic solution ; Averaging method ; Non-smooth diferential system ; Discontinuous diferential system ; Uniform isochronous center |
| Publicat a: | Revista Matemática Iberoamericana, Vol. 33, Issue 4 (2017) , p. 1247-1265, ISSN 0213-2230 |
17 p, 362.7 KB |
