1998
DOI: 10.1088/0954-898x/9/4/009
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Attractor switching by neural control of chaotic neurodynamics

Abstract: Chaotic attractors of discrete-time neural networks include in nitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback c o n trol. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementati… Show more

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Cited by 13 publications
(6 citation statements)
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“…The SO(2)-based CPG is a versatile recurrent neural network consisting of two fully-connected standard additive discretetime neurons N 0 and N 1 , both using a sigmoid transfer function. The SO(2) oscillator can exhibit various dynamical behaviors (e.g., periodic patterns with different frequencies, chaotic patterns, and hysteresis effects [24], [25], [26]) by changing its synaptic weights through manual control or sensory feedback. These dynamical network behaviors can subsequently be exploited for complex locomotion (e.g., chaotic leg movement for self-untrapping of a leg from a hole in the ground [27], walking at different frequencies [28]).…”
Section: A Central Pattern Generator (Cpg)mentioning
confidence: 99%
“…The SO(2)-based CPG is a versatile recurrent neural network consisting of two fully-connected standard additive discretetime neurons N 0 and N 1 , both using a sigmoid transfer function. The SO(2) oscillator can exhibit various dynamical behaviors (e.g., periodic patterns with different frequencies, chaotic patterns, and hysteresis effects [24], [25], [26]) by changing its synaptic weights through manual control or sensory feedback. These dynamical network behaviors can subsequently be exploited for complex locomotion (e.g., chaotic leg movement for self-untrapping of a leg from a hole in the ground [27], walking at different frequencies [28]).…”
Section: A Central Pattern Generator (Cpg)mentioning
confidence: 99%
“…The SO(2)-oscillator is a neural network consisting of only two fully-connected standard additive discrete-time neurons (N 0−1 ), both using a sigmoid transfer function. The SO(2)-oscillator can produce rhythmic output signals with a phase shift of π/2 and display various dynamic behaviors (e.g., periodic patterns with varying frequencies, chaotic patterns, and hysteresis effects (38)(39)(40)) by adjusting its synaptic weights through sensory feedback or manual control. These dynamical network behaviors can subsequently be exploited for complex locomotion modes (e.g., walking at different frequencies (41), chaotic leg movement for self-untrapping of legs that are stuck (42)).…”
Section: To Generate the Basic Rhythmic Signals For Locomotion We Use...mentioning
confidence: 99%
“…Plugging chaos into Artificial Neural Networks (ANN) may enrich its state space with a large number of dynamic behaviors when compared to hopfield networks. These behaviors can be utilized through chaos control methods [18,19,21]. Results of applying such control methods to chaotic attractors showed stabilization into one of its UPOs [7,8,11,20,24].…”
Section: Introductionmentioning
confidence: 99%