Empirical analysis of bifurcations in the full weights space of a two-neuron DTRNN

Cervantes‐Ojeda, Jorge; Gmez-Fuentes, M.; Bernal-Jáquez, R.

doi:10.1016/j.neucom.2017.01.027

Cited by 4 publications

(1 citation statement)

References 9 publications

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“…Indeed, since CTRNNs are known to be universal dynamics approximators [15,26,9], they can also be interpreted as simply convenient building blocks out of which any desired dynamics can be constructed. CTRNNs and closely-related models have been the subject of extensive dynamical analysis [17,39,11,10,21,35,20,12,7,6,41,23,37,32,19,14,8].…”

Section: Introductionmentioning

confidence: 99%

The Global Structure of Codimension-2 Local Bifurcations in Continuous-Time Recurrent Neural Networks

Beer¹

2021

Preprint

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If we are ever to move beyond the study of isolated special cases in theoretical neuroscience, we need to develop more general theories of neural circuits over a given neural model. The present paper considers this challenge in the context of continuous-time recurrent neural networks (CTRNNs), a simple but dynamically-universal model that has been widely utilized in both computational neuroscience and neural networks. Here we extend previous work on the parameter space structure of codimension-1 local bifurcations in CTRNNs to include codimension-2 local bifurcation manifolds. Specifically, we derive the necessary conditions for all generic local codimension-2 bifurcations for general CTRNNs, specialize these conditions to circuits containing from one to four neurons, illustrate in full detail the application of these conditions to example circuits, derive closed-form expressions for these bifurcation manifolds where possible, and demonstrate how this analysis allows us to find and trace several global codimension-1 bifurcation manifolds that originate from the codimension-2 bifurcations.

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Section: Introductionmentioning

confidence: 99%

The Global Structure of Codimension-2 Local Bifurcations in Continuous-Time Recurrent Neural Networks

Beer¹

2021

Preprint

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Codimension-2 parameter space structure of continuous-time recurrent neural networks

Beer

2022

Biol Cybern

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Beautiful chaotic patterns generated using simple untrained recurrent neural networks under harmonic excitation

et al. 2020

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Empirical analysis of bifurcations in the full weights space of a two-neuron DTRNN

Cited by 4 publications

References 9 publications

The Global Structure of Codimension-2 Local Bifurcations in Continuous-Time Recurrent Neural Networks

The Global Structure of Codimension-2 Local Bifurcations in Continuous-Time Recurrent Neural Networks

Codimension-2 parameter space structure of continuous-time recurrent neural networks

Beautiful chaotic patterns generated using simple untrained recurrent neural networks under harmonic excitation

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