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Dynamic behavior analysis of fractional-order Hindmarsh-Rose neuronal model.
Dong Jun1, Zhang Guang-Jun2, Xie Yong3
1College of Science, Air Force Engineering University, Xi'an, 710051 China ; The First Aeronautical Institute of Air Force, Xinyang, 464000 Henan China.
Cognitive Neurodynamics
|March 14, 2014
Summary
Fractional-order neuronal models offer more accurate depictions of neuron firing rates. This study reveals that fractional-order Hindmarsh-Rose models exhibit distinct firing modes and frequencies compared to integer-order models.
Area of Science:
- Computational Neuroscience
- Mathematical Biology
- Dynamical Systems Theory
Background:
- Experimental data suggests neuronal adaptation aligns with fractional-order calculus.
- Fractional-order models provide more verifiable neuron firing rate dynamics than traditional models.
- The Hindmarsh-Rose model is a well-established mathematical model of neuronal activity.
Purpose of the Study:
- To investigate the dynamic characteristics of the fractional-order Hindmarsh-Rose (HR) neuronal model.
- To compare the dynamics of the fractional-order HR model with its integer-order counterpart.
- To identify how fractional order influences neuronal firing modes and dynamics.
Main Methods:
- Investigated the fractional-order Hindmarsh-Rose (HR) neuronal model.
- Analyzed dynamic characteristics by varying the fractional order.
- Compared the behavior of the fractional-order model against the integer-order HR model.
- Identified firing modes, bifurcation points, and firing frequencies.
Main Results:
- The fractional-order HR model exhibits diverse firing modes (chaotic and periodic) dependent on the fractional order, unlike the single mode in integer-order models.
- The Hopf bifurcation point for the fractional-order model is higher than for the integer-order model.
- Fractional-order models show increased firing frequency compared to integer-order models, with frequency increasing as fractional order decreases.
Conclusions:
- Fractional order is a critical determinant of firing modes in the HR neuronal model.
- The fractional-order HR model presents richer dynamics and distinct bifurcation properties compared to the integer-order version.
- Fractional-order modeling offers a more nuanced understanding of neuronal dynamics, particularly firing frequency and mode transitions.
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