Order parameter for bursting polyrhythms in multifunctional central pattern generators.

Area of Science:

• Computational neuroscience
• Systems neuroscience
• Neural network dynamics

Background:

• Central pattern generator (CPG) networks are crucial for rhythmic motor behaviors.
• Understanding multistability in CPGs is essential for explaining diverse neural outputs.
• Hodgkin-Huxley type neuron models provide a detailed biophysical basis for neuronal dynamics.

Purpose of the Study:

• To investigate the multistability of coexisting bursting patterns in a three-neuron CPG network.
• To determine the factors controlling the switching and bifurcations between different bursting polyrhythms.
• To develop a computationally efficient method for analyzing the network's dynamics.

Main Methods:

• Utilized a network of three reciprocally coupled Hodgkin-Huxley type neurons.
• Analyzed the influence of interneuron temporal characteristics (e.g., duty cycle) and coupling strength asymmetry.
• Reduced the nine-dimensional network dynamics to two-dimensional Poincaré return maps.

Main Results:

• Identified that temporal characteristics and coupling asymmetry dictate the control of bursting polyrhythms.
• Demonstrated the switching and bifurcation mechanisms between different bursting patterns.
• Successfully reduced complex network dynamics to a simplified mapping for analysis.

Conclusions:

• Temporal properties and asymmetric coupling are critical determinants of bursting pattern diversity in CPGs.
• The presented reduction method offers an effective approach for analyzing complex neural network dynamics.
• Findings contribute to a deeper understanding of neural control of rhythmic behaviors.