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Titlebook: Weakly Connected Neural Networks; Frank C. Hoppensteadt,Eugene M. Izhikevich Book 1997 Springer Science+Business Media New York 1997 biolo

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Multiple Andronov-Hopf Bifurcation slow time, and .., .., .., .. ∈ ℂ. In this chapter we study general properties of this canonical model. In particular, we are interested in the stability of the origin .. = … = .. = 0 and in the possibility of in-phase and anti-phase locking.
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Multiple Cusp Bifurcationwhere ′ = ., τ is slow time, .., .., .... are real variables, and σ. = ±1. In this chapter we study some neurocomputational properties of this canonical model. In particular, we use Hirsch’s theorem to prove that the canonical model can work as a globally asymptotically stable neural network (GAS-ty
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Neural Networkseds only local information about the behavior of the neuron near the rest potential. Thus, one can obtain some global information about behavior of a system by performing local analysis. Our nonhyperbolic neural network approach uses this observation.
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Introduction to Canonical Modelscould discourage biologists from using mathematics and/or mathematicians. A reasonable way to circumvent this problem is to derive results that are largely independent of the model and that can be observed in a broad class of models. For example, if one modifies a model by adding more parameters and variables, similar results should hold.
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