# Synchronization - A Universal Concept in Nonlinear Sciences

@inproceedings{Pikovsky2001SynchronizationA, title={Synchronization - A Universal Concept in Nonlinear Sciences}, author={Arkady Pikovsky and Michael Rosenblum and J{\"u}rgen Kurths}, booktitle={Cambridge Nonlinear Science Series}, year={2001} }

Preface 1. Introduction Part I. Synchronization Without Formulae: 2. Basic notions: the self-sustained oscillator and its phase 3. Synchronization of a periodic oscillator by external force 4. Synchronization of two and many oscillators 5. Synchronization of chaotic systems 6. Detecting synchronization in experiments Part II. Phase Locking and Frequency Entrainment: 7. Synchronization of periodic oscillators by periodic external action 8. Mutual synchronization of two interacting periodic…

## 6,573 Citations

### Fundamental Concepts of Synchronization

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Objects with rhythms naturally synchronize. Synchronization is the coordination of events in order to run the system uniformly. Yet the phenomenon went entirely undocumented until 1665. Since the…

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Objects with rhythms naturally synchronize. Synchronization is the coordination of events in order to run the system uniformly. Yet the phenomenon went entirely undocumented until 1665. Since the…

### The Behavior of Synchronized Frequency in Weakly Coupled Nonidentical Periodic Oscillators

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This paper considers synchronization of nonidentical periodic oscillators for different coupling schemes, and explains the different frequency behaviors of directly and indirectly coupled systems by analytically deriving the expressions of synchronized frequency under certain simplifying assumptions.

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### Theoretical Background: Non-Autonomous Systems and Synchronization

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The theoretical framework for the analysis of synchronization between non-autonomous oscillating systems is discussed. Multiple-scale analysis is applied to a phase oscillator model with slowly…

### Frequency and phase synchronization in stochastic systems.

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The relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator is discussed.

### Synchronizing Solvable Chaotic Oscillators

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The analytical solution of solvable chaos is used to quantitatively measure the effect of coupling on the synchronized chaotic systems and the resulting oscillators are characterized by their time-series, return maps, phase portraits and finally by their closed-form analytical solutions.

### Synchronization limit of weakly forced nonlinear oscillators

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Nonlinear oscillators exhibit synchronization (injection-locking) to external periodic forcings, which underlies the mutual synchronization in networks of nonlinear oscillators. Despite its history…

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Abstract
We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to…

### Synchronization domains in arrays of chaotic homoclinic systems

- Physics2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775)
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A rich phenomenology of stable competitive states is observed, including temporal alternation and spatial coexistence of synchronization domains in an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli.