Definition
Nonlinear dynamic systems, even if completely described by deterministic equations, may exhibit unpredictable behavior, in that arbitrarily small deviations in the initial conditions, after sufficient time has passed, lead to completely different behavior. This is referred to as deterministic chaos and has been shown to arise in neural population models (NPM).
Detailed Description
Chaotic Systems
Deterministic chaos occurs in systems completely described by deterministic differential equations. These systems may be quite simple, but they have to be nonlinear and live in phase spaces of at least three dimensions (Poincaré-Bendixson theorem). Chaos means that arbitrarily small differences in initial conditions nevertheless lead to strongly diverging trajectories of system behavior after some time. Consequently, under any realistic conditions the system’s long-term behavior is unpredictable. In spite of the impossibility to predict the system’s behavior in any single case, the...
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Knösche, T.R. (2014). Chaos, Neural Population Models and. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_54-2
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_54-2
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Latest
Chaos, Neural Population Models and- Published:
- 28 July 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_54-2
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Chaos, Neural Population Models and- Published:
- 07 February 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_54-1