@article{PopovychMaistrenkoMosekildeetal.2000, author = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Transcritical loss of synchronization in coupled chaotic systems}, year = {2000}, language = {en} } @article{KuznetsovNeumannPikovskijetal.2000, author = {Kuznetsov, Sergey P. and Neumann, Eireen and Pikovskij, Arkadij and Sataev, I. G.}, title = {Critical point of tori collision in quasiperiodically forced systems}, year = {2000}, abstract = {We report on a type of scaling behavior in quasiperiodically forced systems. On the parameter plane the critical point appears as a terminal point of the tori-collision bifurcation curve; its location is found numerically with high precision for two basic models, the forced supercritical circle map and the forced quadratic map. The hypothesis of universality, based on renormalization group arguments, is advanced to explain the observed scaling properties for the critical attractor and for the parameter plane arrangement in the neighborhood of the criticality.}, language = {en} } @article{KatzorkePikovskij2000, author = {Katzorke, Ines and Pikovskij, Arkadij}, title = {Chaos and complexity in a simple model of production dynamics}, issn = {1026-0226}, year = {2000}, language = {en} } @article{ZillmerAhlersPikovskij2000, author = {Zillmer, R{\"u}diger and Ahlers, Volker and Pikovskij, Arkadij}, title = {Scaling of Lyapunov exponents of coupled chaotic systems}, year = {2000}, abstract = {We develop a statistical theory of the coupling sensitivity of chaos. The effect was first described by Daido [Prog. Theor. Phys. 72, 853 (1984)]; it appears as a logarithmic singularity in the Lyapunov exponent in coupled chaotic systems at very small couplings. Using a continuous-time stochastic model for the coupled systems we derive a scaling relation for the largest Lyapunov exponent. The singularity is shown to depend on the coupling and the systems' mismatch. Generalizations to the cases of asymmetrical coupling and three interacting oscillators are considered, too. The analytical results are confirmed by numerical simulations.}, language = {en} } @article{PikovskijRosenblumKurths2000, author = {Pikovskij, Arkadij and Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {Phase synchronization in regular and chaotic systems}, issn = {0218-1274}, year = {2000}, language = {en} } @article{GlendinningFeudelPikovskijetal.2000, author = {Glendinning, P. A. and Feudel, Ulrike and Pikovskij, Arkadij and Stark, J.}, title = {The structure of mode-locking regions in quasi-periodically forced circle maps}, year = {2000}, language = {en} } @article{AhlersZillmerPikovskij2000, author = {Ahlers, Volker and Zillmer, R{\"u}diger and Pikovskij, Arkadij}, title = {Statistical theory for the coupling sensitivity of chaos}, isbn = {1-563-96915-7}, year = {2000}, language = {en} } @article{ZillmerAhlersPikovskij2000, author = {Zillmer, R{\"u}diger and Ahlers, Volker and Pikovskij, Arkadij}, title = {Stochastic approach to Lapunov exponents in coupled chaotic systems}, isbn = {3-540-41074-0}, year = {2000}, language = {en} }