Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling.

Area of Science:

• Nonlinear dynamics
• Complex systems
• Condensed matter physics

Background:

• Self-sustained oscillators form complex networks with emergent behaviors.
• Nonlocal interactions in oscillatory systems can lead to intricate spatiotemporal patterns.
• The van der Pol oscillator is a fundamental model for relaxation oscillations.

Purpose of the Study:

• To investigate the emergence of spatiotemporal patterns in a 2D lattice of coupled van der Pol oscillators.
• To analyze the role of nonlocal active nonlinear coupling in pattern formation.
• To understand the influence of repulsive and attractive coupling terms on system dynamics.

Main Methods:

• Modeling a 2D lattice of van der Pol oscillators.
• Implementing nonlocal active nonlinear coupling using a radiophysical element with negative resistance.
• Analyzing the effects of varying coupling parameters and nonlinearity on emergent patterns.
• Identifying standing waves, periodic dynamics, and chimera states.

Main Results:

• The system exhibits only standing waves and periodic dynamics, with no propagating waves.
• A variety of spatiotemporal patterns, including regular and complex cluster structures (chimera states), emerge with varied coupling parameters.
• The repulsive linear coupling term promotes new periodic states, while the attractive nonlinear term moderates this effect.
• Coupling nonlinearity significantly influences the observed spatiotemporal dynamics.

Conclusions:

• Nonlocal active nonlinear coupling in oscillatory lattices can generate complex spatiotemporal patterns like chimera states.
• The interplay between repulsive and attractive coupling components is crucial for pattern formation.
• The study demonstrates the rich dynamics achievable in coupled oscillator systems, offering insights into complex system behavior.