Controlled perturbation-induced switching in pulse-coupled oscillator networks
| Autor: | Fabio Schittler Neves, Marc Timme |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Spiking neural network Physics Computation FOS: Physical sciences Computer Science - Neural and Evolutionary Computing General Physics and Astronomy Perturbation (astronomy) Statistical and Nonlinear Physics Pulse coupled oscillator Topology Nonlinear Sciences - Adaptation and Self-Organizing Systems Modeling and Simulation Attractor Homogeneous space Neural system Neural and Evolutionary Computing (cs.NE) Adaptation and Self-Organizing Systems (nlin.AO) Mathematical Physics Saddle |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 42:345103 |
| ISSN: | 1751-8121 1751-8113 |
| DOI: | 10.1088/1751-8113/42/34/345103 |
| Popis: | 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 those 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. |
| Databáze: | OpenAIRE |
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