Rössler-network with time delay: Univariate impulse pinning synchronization

Area of Science:

• Chaos Theory
• Network Synchronization
• Control Systems

Background:

• Dynamical systems, like the Rössler system, are fundamental in understanding complex behaviors.
• Network synchronization is crucial for controlling emergent behaviors in interconnected systems.
• Pinning control, using a small set of nodes, offers an efficient strategy for network regulation.

Purpose of the Study:

• To investigate the pinning synchronization of a coupled Rössler network with time delay.
• To develop and validate a univariate impulse control strategy for network regulation.
• To honor the scientific contributions of Rössler through research on his benchmark system.

Main Methods:

• Utilizing Lyapunov theory to establish conditions for asymptotic stability.
• Developing a univariate impulse control technique for synchronization.
• Employing network simulations to verify analytical results.

Main Results:

• A theorem proving the asymptotic stability of synchronization in the Rössler network was derived.
• The effectiveness of the univariate impulse pinning controller was demonstrated through simulations.
• Successful synchronization of the coupled Rössler network was achieved.

Conclusions:

• The proposed univariate impulse control method is effective for achieving pinning synchronization in delayed Rössler networks.
• The theoretical analysis, supported by simulations, confirms the stability of the synchronized network.
• This work provides a valuable control strategy for complex dynamical networks.