Phase diagrams and dynamics of a computationally efficient map-based neuron model.

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Dynamical Systems Theory

Background:

• Standard neuron models often present trade-offs between computational efficiency, analytical tractability, and the richness of their dynamical behaviors.
• Existing models may have large parameter spaces or limited repertoires of autonomous and excitable dynamics.

Purpose of the Study:

• To introduce a new map-based neuron model derived from the dynamical perceptron family.
• To achieve a superior compromise between computational efficiency, analytical tractability, reduced parameter space, and diverse dynamical behaviors.
• To characterize the model's dynamical repertoire and compare it with existing neuron models.

Main Methods:

• Derivation of a novel map-based neuron model from the dynamical perceptron family.
• Analytical and computational calculation of bifurcation and phase diagrams.
• Characterization of autonomous and excitable dynamical behaviors.
• Comparison of the new model's features against standard neuron models in the literature.

Main Results:

• The proposed model demonstrates an optimal balance of computational efficiency, analytical tractability, and a reduced parameter space.
• Bifurcation and phase diagrams reveal a rich repertoire of autonomous and excitable dynamical behaviors.
• A novel regime of cardiac spikes, characterized by nonchaotic aperiodic behavior, has been identified.

Conclusions:

• The new map-based neuron model offers a powerful and versatile tool for studying neuronal dynamics.
• The model's ability to exhibit complex behaviors, including the newly discovered cardiac spike regime, makes it a valuable addition to computational neuroscience.
• Its favorable balance of properties facilitates both theoretical analysis and computational simulations of neural activity.