Ir al contenido

Documat


On the Stability of Hybrid Polycycles

  • Autores: Paulo Santana, Leonardo Serantola
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen
    • In this paper we provide the stability of generic polycycles of hybrid planar vector fields, extending previous known results in the literature. The polycycles considered here may have hyperbolic saddles, tangential singularities and jump singularities.

  • Referencias bibliográficas
    • 1. Akhmet, M.: Nonlinear hybrid continuous/discrete-time models. Atlantis Stud. Math. Eng. Sci. 8 (2011)
    • 2. Andrade, K., Gomide, O., Novaes, D.: Bifurcation diagrams of global connections in Filippov systems. Nonlinear Anal. Hybrid Syst. 50, Paper...
    • 3. Andrade, K., Jeffrey, M.R., Martins, R.M., Teixeira, M.A.: Homoclinic boundary-saddle bifurcations in planar nonsmooth vector fields. Int....
    • 4. Belykh, I., Kuske, R., Porfiri, M., Simpson, D.J.W.: Beyond the Bristol book: advances and perspectives in non-smooth dynamics and applications....
    • 5. di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczyk, P.: Piecewise-smooth dynamical systems: theory and applications. Appl. Math. Sci....
    • 6. Buzzi, C., Carvalho, T., Euzébio, R.: On Poincaré–Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields. Publ....
    • 7. Buzzi, C., Carvalho, T., Teixeira, M.: On three-parameter families of Filippov systems - the fold-saddle singularity. Int. J. Bifur. Chaos...
    • 8. Buzzi, C., Gasull, A., Santana, P.: On the cyclicity of hyperbolic polycycles. Preprint, arXiv:2407.20721 (2024)
    • 9. Branicky, M.: Introduction to Hybrid Systems, Handbook of Networked and Embedded Control Systems, pp. 91–116 (2005)
    • 10. Cherkas, L.: The stability of singular cycles. Differencial’nye Uravnenija, 1012–1017 (1968)
    • 11. Dukov, A.: Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles. Mat. Sb. 214(2), 90–111 (2023)
    • 12. Dukov, A.: Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles, translation in Sb. Mathematics 214(2),...
    • 13. Dulac, H.: Sur les cycles limites. Bull. Soc. Math. France 51, 45–188 (1923)
    • 14. Filippov, A.: Differential equations with discontinuous righthand sides. Translated from the Russian Math. Appl. (Soviet Ser.), 18 Kluwer...
    • 15. Gasull, A., Mañosa, V., Mañosas, F.: Stability of certain planar unbounded polycycles. J. Math. Anal. Appl. 269(1), 332–351 (2002)
    • 16. Han, M., Hu, S., Liu, X.: On the stability of double homoclinic and heteroclinic cycles. Nonlinear Anal. 53(5), 701–713 (2003)
    • 17. Han, M., Wu, Y., Bi, P.: Bifurcation of limit cycles near polycycles with n vertices. Chaos Solitons Fractals 22(2), 383–394 (2004)
    • 18. Han, M., Zhou, X.: On stability discrimination of limit cycles for piecewise smooth systems. Acta Math. Sin. (Engl. Ser.) 40(7), 1785–1803...
    • 19. Han, M., Zhu, H.: The loop quantities and bifurcations of homoclinic loops. J. Differ. Equ. 234(2), 339–359 (2007)
    • 20. Jacquemard, A., Khechichine-Mourtada, F., Mourtada, A.: Algorithmes formels appliqués à l’étude de la cyclicité d’un polycycle algébrique...
    • 21. Li, Z., Liu, X.: Impact limit cycles in the planar piecewise linear hybrid systems. Commun. Nonlinear Sci. Numer. Simul. 119, Paper No....
    • 22. Li, S., Ma, W., Zhang, W., Hao, Y.: Melnikov method for a class of planar hybrid piecewise-smooth systems. Int. J. Bifur. Chaos Appl....
    • 23. Li, Y., Wei, Z., Zhang, W., Kapitaniak, T.: Melnikov-type method for chaos in a class of hybrid piecewise-smooth systems with impact and...
    • 24. Li, Y., Wei, Z., Zhang, W., Yi, M.: Melnikov-type method for a class of hybrid piecewise-smooth systems with impulsive effect and noise...
    • 25. Liu, S., Han, M.: Limit cycle bifurcations near double homoclinic and double heteroclinic loops in piecewise smooth systems. Chaos Solitons...
    • 26. Liu, S., Han, M.: Homoclinic and heteroclinic bifurcations in piecewise smooth systems via stabilitychanging method. Comput. Appl. Math....
    • 27. Llibre, J., Santana, P.: Limit cycles and chaos in planar hybrid systems. Commun. Nonlinear Sci. Numer. Simul. 140, Paper No. 108382 (2025)
    • 28. Llibre, J., Teixeira, M.: Piecewise linear differential systems with only centers can create limit cycles? Nonlinear Dynam. 91(1), 249–255...
    • 29. Marin, D., Villadelprat, J.: Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: local setting. J. Differ....
    • 30. Marin, D., Villadelprat, J.: Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting. J....
    • 31. Marin, D., Villadelprat, J.: On the cyclicity of Kolmogorov polycycles. Electron. J. Qual. Theory Differ. Equ. Paper No. 35 (2022)
    • 32. Marin, D., Villadelprat, J.: Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: coefficient properties....
    • 33. Mourtada, A.: Cyclicite finie des polycycles hyperboliques de champs de vecteurs du plan mise sous forme normale, Bifurcations of planar...
    • 34. Mourtada, A.: Degenerate and non-trivial hyperbolic polycycles with two vertices. J. Differ. Equ. 113(1), 68–83 (1994)
    • 35. Mourtada, A.: Bifurcation de cycles limites au voisinage de polycycles hyperboliques et génériques à trois sommets. Ann. Fac. Sci. Toulouse...
    • 36. Novaes, D., Rondon, G.: Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles. Nonlinearity...
    • 37. Novaes, D., Rondon, G.: On limit cycles in regularized Filippov systems bifurcating from homocliniclike connections to regular-tangential...
    • 38. Novaes, D., Teixeira, M., Zeli, I.: The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov...
    • 39. Perko, L.: Differential Equations and Dynamical Systems, Third edition Texts Appl. Math. 7, SpringerVerlag, New York (2001)
    • 40. Roussarie, R.: Bifurcations of planar vector fields and Hilbert’s sixteenth problem. Mod. Birkhäuser Class. Birkhäuser/Springer, Basel...
    • 41. Schaft, A., Schumacher, H.: An Introduction to Hybrid Dynamical Systems. Lect. Notes Control Inf. Sci., 251. Springer-Verlag London, Ltd.,...
    • 42. Sheng, L., Han, M., Tian, Y.: On the number of limit cycles bifurcating from a compound polycycle. Int. J. Bifur. Chaos Appl. Sci. Eng....
    • 43. Samoilenko, A.M., Perestyuk, N.A.: Impulsive differential equations. World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises 14 (1995)
    • 44. Santana, P.: Stability and cyclicity of polycycles in non-smooth planar vector fields. Qual. Theory Dyn. Syst. 22(4), Paper No. 142 (2023)
    • 45. Sotomayor, J.: Curvas Definidas por Equações Diferenciais no Plano. Instituto de Matemática Pura e Aplicada, Rio de Janeiro (1981)
    • 46. Wei, Z., Li, Y., Moroz, I., Zhang, W.: Melnikov-type method for a class of planar hybrid piecewisesmooth systems with impulsive effect...

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno