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CPG Stability Characterization by a Numerical Modified Floquet Technique

Nicholas Szczecinski1*, Alexander Lonsberry1 and Roger Quinn1
  • 1 Case Western Reserve University, Mechanical Engineering, United States

The response of simulated half-center oscillator circuits under perturbing stimuli is investigated. This research is part of ongoing work to construct controllers for legged robots that allow them to adapt to very different terrains based exclusively on biological neural networks. Transitioning and adapting to different terrains is a common problem for current legged vehicles. In addition to the robotics objectives, the project also promises to test hypotheses on nervous system function.

Central pattern generators (CPGs) are one critical neurological sub-system that drives locomotive behavior. The CPG structure studied here is a pair of tonically driven neurons connected via facilitating inhibitory synapses. The CPG is perturbed by an exponentially decaying current meant to mimic a single spike of synaptic current from an afferent cell. A modified Floquet multiplier method is implemented to reveal characteristic stability properties of the neural circuit. These experiments provide quantitative insight into the system’s behavior under perturbation, specifically: 1) what phase and magnitude stimuli will cause the cyclic bursting action in the CPG to cease indefinitely, 2) what is the phase shift of the original CPG signal if the perturbed oscillator returns to its original limit cycle, and 3) if and over what time scale does the perturbed signal return to the original cycle. Analyses reveal some very insightful general results, which serve as rules for constructing larger circuits that maintain stability in the presence of stimulation. We present simulations of these larger circuits with varied stimuli to show that the circuit construction rules indeed lead to stability. All simulated neurons used are modified versions of the leaky integrate and fire neuron model. All experimentation is conducted in a numerical simulation engine written by the authors that runs trials sequentially while sweeping through neuron and synapse parameter space.

Acknowledgements

This research was funded by a grant from DARPA as a part of the Maximum Mobility and Manipulation program.

References

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Keywords: CpG, Floquet, integrate and fire, Limit Cycle, stability

Conference: Tenth International Congress of Neuroethology, College Park. Maryland USA, United States, 5 Aug - 10 Aug, 2012.

Presentation Type: Poster (but consider for student poster award)

Topic: Computational Modeling

Citation: Szczecinski N, Lonsberry A and Quinn R (2012). CPG Stability Characterization by a Numerical Modified Floquet Technique. Conference Abstract: Tenth International Congress of Neuroethology. doi: 10.3389/conf.fnbeh.2012.27.00215

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Received: 29 Apr 2012; Published Online: 07 Jul 2012.

* Correspondence: Mr. Nicholas Szczecinski, Case Western Reserve University, Mechanical Engineering, Cleveland, United States, nss36@case.edu