In this article, we study the phenomenon of -synchronization for a quasilinear system governed by -Laplacian, . We obtain this result through the upper semicontinuity of the attractors associated with the systems and the synchronicity property of the limit system.
AfraimovichV. S.RodriguesH. M. (1998). Uniform dissipativeness and synchronization of nonautonomous equations. International Conference on Differential Equations (Lisboa 1995), 3–17.
2.
BoccalettiS.PisarchikA. N.Del GenioC. I.AmannA. (2018). Synchronization: From coupled systems to complex networks. Cambridge University Press.
3.
BonannoG. (2002). A minimax inequality and its applications to ordinary differential equations. Journal of Mathematical Analysis and Applications, 270, 210–229.
4.
BrézisH. (1973). Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. American Elsevier Publishing.
5.
BruschiS. M.GentileC. B.PrimoM. R. T. (2010). Continuity properties on for -Laplacian parabolic problems. Nonlinear Analysis, 72, 1580–1588.
6.
CaraballoT.KloedenP. E. (2005). The persistence of synchronization under environmental noise. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2059), 2257–2267.
7.
CarvalhoA. N.PrimoM. R. T. (2000). Boundary synchronization in parabolic problems with nonlinear boundary conditions. Dynamics of Continuous, Discrete and Impulsive Systems, 7(4), 541–560.
8.
CarvalhoA. N.RodriguesH. M.DlotkoT. (1998). Upper semicontinuity of attractors and synchronization. Journal of Mathematical Analysis and Applications, 220, 13–41.
9.
GameiroM. F.RodriguesH. M. (2001). Applications of robust synchronization to communication systems. Applicable Analysis, 79(1–2), 21–45.
10.
GhoshD.MarwanN.SmallM.ZhouC.HeitzigJ.KoseskaA.JiP.KissI. Z. (2024). Recent achievements in nonlinear dynamics, synchronization, and networks. Chaos (Woodbury, N.Y.), 100401.
11.
HaleJ. K. (1988). Asymptotic Behavior of Dissipative Systems. (Mathematical Surveys and Monographs, Vol. 25). American Mathematical Society.
12.
HaleJ. K. (1997). Diffusive coupling, dissipation, and synchronization. Journal of Dynamics and Differential Equations, 9, 1–52.
13.
KloedenP. E. (2003). Synchronization of nonautonomous dynamical systems. Electronic Journal of Differential Equations, 2003, 1–10.
14.
KloedenP. E.PavaniR. (2009). Dissipative synchronization of nonautonomous and random systems. GAMM-Mitt, 32(1), 80–92.
15.
LadyzhenskayaO. A. (1991). Attractors for semigroups and evolution equations. Cambridge University Press.
16.
ÖtaniM. (1977). On existence of strong solutions for . Journal of the Faculty of Science, University of Tokyo. Section IA, Mathematics, 24, 575–605.
17.
OuardiH. E.HachimiA. E. (2006). Attractors for a class of doubly nonlinear parabolic systems. Electronic Journal of Qualitative Theory of Differential Equations, 2006, 1–15.
18.
PereiraA. C.MoussaC. B. G.MiyagakiO. H. (2015). An example of noncontinuous attractors. Journal of Evolution Equations, 15, 979–1000.
19.
RodriguesH. M. (1996). Abstract methods for synchronization and applications. Applicable Analysis, 62, 263–296.
20.
RodriguesH. M.AlbertoL. F. C.BretasN. G. (2001). Uniform invariance principle and synchronization: Robustness with respect to parameter variation. Journal of Differential Equations, 169(1), 228–254.
21.
StrogatzS. H. (2003). Sync: The emerging science of spontaneous order. Hyperion.
22.
TakeuchiS.YamadaY. (2000). Asymptotic properties of a reaction-diffusion equation with degenerate -Laplacian. Nonlinear Analysis, 42, 41–61.
23.
TemamR. (1997). Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Applied Mathematical Sciences, Vol. 68). Springer-Verlag.
24.
VrabieI. I. (1995). Compactness methods for nonlinear evolutions. John Wiley & Sons.
