TY  - JOUR
A1  - Zillmer, Rüdiger
A1  - Ahlers, Volker
A1  - Pikovskij, Arkadij
T1  - Scaling of Lyapunov exponents of coupled chaotic systems
N2  - 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.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zillmer, Rüdiger
A1  - Ahlers, Volker
A1  - Pikovskij, Arkadij
T1  - Stochastic approach to Lapunov exponents in coupled chaotic systems
Y1  - 2000
SN  - 3-540-41074-0
ER  - 
TY  - JOUR
A1  - Ahlers, Volker
A1  - Zillmer, Rüdiger
A1  - Pikovskij, Arkadij
T1  - Statistical theory for the coupling sensitivity of chaos
Y1  - 2000
SN  - 1-563-96915-7
ER  - 
TY  - JOUR
A1  - Ahlers, Volker
A1  - Zillmer, Rüdiger
A1  - Pikovskij, Arkadij
T1  - Lyapunov exponents in disordered chaotic systems : avoided crossing and level statistics
N2  - The behavior of the Lyapunov exponents (LEs) of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, qualitatively similar to the behavior of energy levels in quantum chaos. Recent results for the coupling dependence of the LEs of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small values. The results are interpreted in terms of the random matrix theory.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Ahlers, Volker
A1  - Pikovskij, Arkadij
T1  - Critical Properties of the Synchronization Transition in Space-Time Chaos
N2  - We study two coupled spatially extended dynamical systems which exhibit space-time chaos. The transition to the synchronized state is treated as a nonequilibrium phase transition, where the average synchronization error is the order parameter. The transition in one-dimensional systems is found to be generically in the universality class of the Kardar- Parisi-Zhang equation with a growth-limiting term ("bounded KPZ"). For systems with very strong nonlinearities in the local dynamics, however, the transition is found to be in the universality class of directed percolation.
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Ginelli, F.
A1  - Ahlers, Volker
A1  - Livi, R.
A1  - Mukamel, D.
A1  - Pikovskij, Arkadij
A1  - Politi, Antonio
A1  - Torcini, A.
T1  - From multiplicative noise to directed percolation in wetting transitions
N2  - A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behavior observed along the transition line changes from a directed-percolation type to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions. Mean-field arguments and the mapping on yet a simpler model provide some further insight on the overall scenario
Y1  - 2003
SN  - 1063-651X
ER  -