Controlled perturbation-induced switching in pulse-coupled oscillator networks

Schittler Neves, Fabio; Timme, Marc

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Controlled perturbation-induced switching in pulse-coupled oscillator networks

Schittler Neves, F., & Timme, M. (2009). Controlled perturbation-induced switching in pulse-coupled oscillator networks. Journal of Physics A, 42: 345103.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0029-12D1-5 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0029-12D2-3

Genre: Journal Article

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Schittler Neves, Fabio¹, Author
Timme, Marc², Author

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1Research Group Theoretical Neurophysics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063289
2Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063295

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Abstract: Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in these networks and enable novel kinds of neural computations. For small networks of coupled oscillators, we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators, we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.

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Language(s): eng - English

Dates: Date issued: 2009-08-10

Publication Status: Issued

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Rev. Type: Peer

Identifiers: eDoc: 449365

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Title: Journal of Physics A

Alternative Title : J. Phys. A: Math. Theor.

Source Genre: Journal

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Pages: - Volume / Issue: 42 Sequence Number: 345103 Start / End Page: - Identifier: -