Complete synchronization and generalized synchronization of one-way coupled time-delay systems.

¹Temasek Laboratories, National University of Singapore, Singapore 119260.

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

|October 4, 2003

Summary

Generalized synchronization (GS) in time-delay systems can be achieved using a single scalar signal. Parameter resonance effects enable stable synchronization with reduced coupling by matching system delay times.

Area of Science:

Nonlinear Dynamics
Chaos Theory
Control Systems

Background:

Time-delay systems are prevalent in various scientific and engineering fields.
Synchronization phenomena, including generalized synchronization (GS), are crucial for understanding complex system behaviors.
Controlling and recovering states in systems with time delays presents significant challenges.

Purpose of the Study:

To investigate the conditions for complete synchronization and generalized synchronization (GS) in one-way coupled time-delay systems.
To analyze the influence of delay times on the synchronization threshold.
To explore the potential applications of observed synchronization features in system recovery.

Main Methods:

Analysis of one-way coupled time-delay systems.
Mathematical formulation and theoretical investigation of synchronization criteria.
Numerical simulations to observe synchronization dynamics and parameter resonance effects.

Main Results:

Generalized synchronization (GS) can be achieved using a single scalar signal.
A parameter resonance effect was identified, where synchronization thresholds depend on the delay times of the driving and driven systems.
Stable synchronization is achievable with smaller coupling strengths when system delays are in resonance.
Near chaos synchronization, desynchronization exhibits periodic bursts with a period equal to the driven system's delay time.

Conclusions:

The study demonstrates a method for achieving generalized synchronization in time-delay systems via a single scalar signal.
The parameter resonance effect offers a strategy for enhancing synchronization stability and reducing coupling requirements.
The observed dynamics provide insights applicable to the recovery and control of time-delay systems.

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Area of Science:

Background:

Purpose of the Study:

Main Methods:

Main Results:

Conclusions:

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