Coupling multistable systems: uncertainty due to the initial positions on the attractors

• Autorzy: Kuzma P. , Kapitaniak M. , Kapitaniak T.
• Języki publikacji: EN

Abstrakty

EN

We consider the coupling of multistable nonidentical systems. For small values of the coupling coefficient the behavior of the coupled system strongly depends on the actual position of trajectories on their attractors in the moment when the coupling is introduced. After reaching the coupling threshold value, this dependence disappears. We give an evidence that this behavior is robust as it exists for a wide range of parameters and different types of coupling. We argue why this behavior cannot be considered as a dependence on the initial conditions.

Słowa kluczowe

EN

coupled systems; synchronization; attractors

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2014
• Tom: Vol. 52 nr 1
• Strony: 281--284
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Kuzma P.

• Technical University of Lodz, Division of Dynamics, Poland

autor

Kapitaniak M.

• Technical University of Lodz, Division of Dynamics, Łódź, Poland and Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Scotland

autor

Kapitaniak T.

• Technical University of Lodz, Division of Dynamics, Łódź, Poland

Bibliografia

• 1. Casas G.A., Rech P.C., 2012, Multistability annihilation in the Henon map through parameters modulation, Communications in Nonlinear Science and Numerical Simulation, 17, 2570-2578
• 2. Chudzik A., Perlikowski P., Stefanski A., Kapitaniak T., 2011, Multistability and Rare attractors in van der Pol-Duffing oscillator, International Journal of Bifurcation and Chaos, 21, 1907-1912
• 3. Feudel U., 2008, Complex dynamics in multistable systems, International Journal of Bifurcation and Chaos, 18, 1607-1626
• 4. Feudel U., Grebogi C., Poon L., Yorke J.A., 1998, Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors, Chaos Solitons Fractas, 9, 171-180
• 5. Martínez-Zérega B.E., Pisarchik A.N., 2012, Stochastic control of attractor preferencje in a multistable system, Communications in Nonlinear Science and Numerical Simulation, 17, 4023-4028
• 6. Pisarchik A.N., Jaimes-Réategui R., Villalobos-Salazar J.R., Garčıa-López J.H., Boccaletti S., 2006, Synchronization of chaotic systems with coexisting attractors, Physical Review Letters, 96, 244102.
• 7. Sausedo-Solorio J.M., Pisarchik A.N., 2011, Dynamics of unidirectionally coupled bistable Hénon maps, Physics Letters A, 375, 3677-3681