Giberti, Claudio; Vernia, Cecilia Tori breakdown in coupled map lattices. (English) Zbl 1044.37050 Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 4, 765-781 (2002). Summary: We present a numerical study of invariant tori in a lattice of coupled logistic maps. In particular, we are interested in bifurcations leading to chaos. Here, we consider six different examples of tori breakdown: two of them completely confirm the theory of Afraimovich and Shilnikov, while the others appear peculiar to the model. MSC: 37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:Coupled map lattices; tori breakdown; Afraimovich scenario; Shilnikov scenario; bifurcation of invariant tori; numerical simulations; chaotic behavior; period-doubling cascades PDFBibTeX XMLCite \textit{C. Giberti} and \textit{C. Vernia}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 4, 765--781 (2002; Zbl 1044.37050) Full Text: DOI References: [1] Afraimovich V. S., Amer. Math. Soc. Transl. 149 pp 201– · Zbl 0751.58024 · doi:10.1090/trans2/149/12 [2] DOI: 10.1103/PhysRevLett.70.3408 · doi:10.1103/PhysRevLett.70.3408 [3] DOI: 10.1142/S0218127494000423 · Zbl 0870.58050 · doi:10.1142/S0218127494000423 [4] DOI: 10.1007/978-3-642-57884-7 · doi:10.1007/978-3-642-57884-7 [5] DOI: 10.1007/BF02429852 · Zbl 0872.58049 · doi:10.1007/BF02429852 [6] DOI: 10.1088/0951-7715/1/4/001 · Zbl 0679.58028 · doi:10.1088/0951-7715/1/4/001 [7] DOI: 10.1063/1.165870 · Zbl 1055.37560 · doi:10.1063/1.165870 [8] L. A. Bunimovich and Ya. G. Sinai, Theory and Applications of Coupled Map Lattices, ed. K. Kaneko (John Wiley, 1993) pp. 169–189. · Zbl 0791.60099 [9] DOI: 10.1088/0951-7715/9/5/010 · Zbl 0895.58037 · doi:10.1088/0951-7715/9/5/010 [10] DOI: 10.1016/S0167-2789(96)00249-7 · Zbl 1194.82048 · doi:10.1016/S0167-2789(96)00249-7 [11] Collet P., Iterated Maps on The Interval as Dynamical Systems (1980) · Zbl 0458.58002 [12] Curry J., Lecture Notes in Mathematics 668 pp 48– (1978) · doi:10.1007/BFb0101779 [13] DOI: 10.1142/S0218127493001185 · Zbl 0890.58076 · doi:10.1142/S0218127493001185 [14] DOI: 10.1063/1.166042 · Zbl 1055.37523 · doi:10.1063/1.166042 [15] Gotlub J. P., J. Fluid. Mech. 100 pp 449– [16] DOI: 10.1016/0167-2789(89)90117-6 · doi:10.1016/0167-2789(89)90117-6 [17] DOI: 10.1007/BF02677976 · Zbl 0879.58054 · doi:10.1007/BF02677976 [18] DOI: 10.1142/9789812798596 · doi:10.1142/9789812798596 [19] Vernia C., Rand. Comput. Dyn. 2 pp 305– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.