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Synchronization and desynchronization under the influence of quasiperiodic forcing
Eireen Neumann1, Irina Sushko, Yuri Maistrenko
1Department of Physics, University of Potsdam, Am Neuen Palais, PF 601553, D-14415 Potsdam, Germany.
Summary
Quasiperiodic forcing shrinks synchronization regions in coupled logistic maps. This leads to desynchronization through blowout bifurcations of synchronized attractors, resulting in chaotic dynamics.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Complex systems
Background:
- Synchronization is a fundamental phenomenon in coupled dynamical systems.
- Quasiperiodic forcing introduces complex dynamics and can alter synchronization properties.
- Understanding desynchronization mechanisms is crucial for analyzing system stability.
Purpose of the Study:
- To investigate the impact of quasiperiodic forcing on the synchronization of coupled logistic maps.
- To identify the mechanisms leading to desynchronization under quasiperiodic forcing.
- To characterize the bifurcations causing the loss of synchronization.
Main Methods:
- Utilizing two coupled quasiperiodically forced logistic maps as a model system.
- Analyzing the parameter space to identify regions of synchronization and desynchronization.
- Investigating blowout bifurcations of synchronized attractors.
Main Results:
- Quasiperiodic forcing significantly reduces the parameter space region for synchronization.
- Loss of transverse stability in synchronized attractors triggers desynchronization.
- Two distinct types of blowout bifurcations were identified, leading to desynchronized chaotic attractors.
Conclusions:
- Quasiperiodic forcing destabilizes synchronized states in coupled maps.
- Blowout bifurcations are the primary mechanism for desynchronization in this system.
- The study reveals complex transitions from synchronized quasiperiodic and nonchaotic attractors to desynchronized chaos.