Ghost attractors in blinking Lorenz and Hindmarsh-Rose systems.

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Computational Neuroscience

Background:

• Blinking systems involve random switching between autonomous subsystems.
• Non-stationary attractors in blinking systems can differ from subsystem attractors.
• Ghost attractors arise from averaged systems in fast-switching scenarios.

Purpose of the Study:

• Investigate non-stationary and ghost attractors in fast-switching blinking systems.
• Demonstrate emergent dynamics in blinking systems not present in individual subsystems.
• Analyze the impact of switching period on dynamical behavior.

Main Methods:

• Analysis of blinking systems with fast stochastic switching.
• Numerical approximation of invariant measures for blinking and averaged systems.
• Study of Lorenz and Hindmarsh-Rose models under blinking conditions.

Main Results:

• Fast switching in Lorenz systems produced a ghost chaotic attractor from stable equilibria.
• A blinking Hindmarsh-Rose model exhibited bursting activity despite tonic spiking stimuli.
• Dynamical behavior changes were analyzed with increasing stochastic switching periods.

Conclusions:

• Fast switching can induce complex ghost attractors and novel dynamics.
• Blinking systems offer a route to emergent phenomena in nonlinear dynamics.
• Numerical estimates confirm the proximity of non-stationary and ghost attractors.