How to induce multiple delays in coupled chaotic oscillators?

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Complex Systems

Background:

• Lag synchronization is a key phenomenon in various coupled systems, characterized by a consistent time shift between state variables.
• Existing research primarily focuses on single lag configurations within coupled systems.

Purpose of the Study:

• To investigate the induction of multiple lag configurations in coupled systems.
• To design a coupling method enabling different time shifts between distinct pairs of state variables.
• To demonstrate the physical realization of multiple lag synchronization.

Main Methods:

• Development of a novel coupling design to achieve multiple lag synchronization.
• Numerical simulations using the Rössler system and the slow-fast Hindmarsh-Rose neuron model.
• Experimental validation using an electronic circuit with two Sprott systems.

Main Results:

• Successfully induced multiple lag configurations in coupled systems.
• Demonstrated that different pairs of state variables can achieve distinct time shifts.
• Validated the theoretical findings through numerical simulations and physical circuit implementation.

Conclusions:

• The proposed coupling design effectively enables multiple lag synchronization in complex systems.
• Multiple lag synchronization offers a new paradigm for controlling and understanding coupled dynamical systems.
• The findings have implications for fields utilizing coupled oscillators and networks, such as neuroscience and secure communications.