Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Nonlinear Dynamics

Background:

• Interior crises involve discontinuous changes in chaotic attractor size.
• These crises occur when unstable periodic orbits collide with the chaotic attractor.

Purpose of the Study:

• To investigate a novel chaos-chaos transition in the Hindmarsh-Rose neuron model.
• To characterize the transition between bursting and spiking dynamics.
• To understand the underlying mechanism of this transition.

Main Methods:

• Numerical simulations of the Hindmarsh-Rose model.
• Theoretical analysis using a simplified one-dimensional map.
• Investigation of attractor size and qualitative property changes.

Main Results:

• Evidence for a sudden but continuous chaos-chaos transition in attractor size.
• Observed qualitative changes in system properties during the transition.
• Identified the transition mechanism via a one-dimensional map exhibiting a crossover between universal behaviors.

Conclusions:

• The Hindmarsh-Rose model exhibits a unique chaos-chaos transition at the bursting-spiking dynamics boundary.
• This transition is characterized by continuous changes in attractor size and qualitative property shifts.
• A simplified one-dimensional map elucidates the crossover mechanism driving this neuronal dynamics transition.