Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

Area of Science:

• Computational neuroscience
• Dynamical systems theory

Background:

• The FitzHugh-Nagumo model is a simplified mathematical model of neuron dynamics.
• Poincare sections are used to analyze the behavior of dynamical systems.

Purpose of the Study:

• To investigate the dynamics of two coupled piece-wise linear one-dimensional monostable maps.
• To understand the effect of diffusive coupling on these maps, particularly in relation to neuron models.

Main Methods:

• Analysis of coupled piece-wise linear one-dimensional monostable maps.
• Association of the single map with the Poincare section of the FitzHugh-Nagumo neuron model.
• Identification of chaotic attractors within invariant phase space regions.

Main Results:

• Diffusive coupling induces the formation of a chaotic attractor.
• The chaotic attractor is situated in an invariant region bounded by saddle point manifolds.
• Observed oscillations display a spike-burst pattern with anti-phase synchronized spiking.

Conclusions:

• Diffusive coupling in simplified neuron models can lead to complex chaotic dynamics.
• The identified chaotic attractor and its spike-burst oscillations offer insights into neural firing patterns.
• Anti-phase synchronization of spiking is a notable emergent behavior in this coupled system.