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Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

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Partial synchronization on a network with different classes of oscillators.

Emmanuel Gräve de Oliveira¹, Thomas Braun

¹Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil. emmanuel.deoliveira@ufrgs.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 1, 2008

Summary

This study demonstrates partial synchronization in a network of non-identical coupled Rössler oscillators. Even with different oscillator dynamics, synchronized states, including primary and secondary synchronization, were achieved.

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Area of Science:

Nonlinear dynamics
Complex systems
Network science

Background:

Synchronization in coupled oscillator networks is well-studied, typically focusing on identical oscillators.
Investigating synchronization in networks with non-identical elements is crucial for understanding complex systems.

Purpose of the Study:

To explore partial synchronization in a network of non-identical coupled Rössler oscillators.
To define and identify primary and secondary synchronization in such a network.

Main Methods:

Utilizing a network of four Rössler oscillators diffusively coupled in a ring formation.
Employing direct numerical integration and transverse Lyapunov exponent computation to analyze synchronization behavior.

Main Results:

Achieved both primary synchronization (identical synchronization within oscillator classes) and secondary synchronization (other partial synchronization patterns).
Demonstrated that networks with distinct oscillator classes can exhibit complex synchronized states.
Presented evidence of riddled basins of attraction, indicating sensitive dependence on initial conditions.

Conclusions:

Partial synchronization is attainable in networks composed of non-identical coupled oscillators.
The proposed Rössler oscillator network model provides a platform for studying diverse synchronization phenomena.
Riddled basins of attraction highlight the complex dynamics and potential unpredictability in such systems.