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Advanced Models of Neural Networks pp 181–190Cite as

Synchronization of Chaotic and Stochastic Neurons Using Differential Flatness Theory

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Abstract

This chapter presents a control method for neuron models that have the dynamics of chaotic oscillators. The proposed chaotic control method makes use of a linearized model of the chaotic oscillator which is obtained after transforming the oscillators dynamic model into a linear canonical form through the application of differential flatness theory . The chapter also analyzes a synchronizing control method (flatness-based control) for stochastic neuron models which are equivalent to particle systems and which can be modeled as coupled stochastic oscillators. It is explained that the kinematic model of the particles can be derived from the model of the quantum harmonic oscillator (QHO) . It is shown that the kinematic model of the particles is a differentially flat system. It is also shown that after applying flatness-based control the mean of the particle system can be steered along a desirable path with infinite accuracy, while each individual particle can track the trajectory within acceptable accuracy levels.

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Authors and Affiliations

  1. Unit of Industrial Automation, Industrial Systems Institute, Rion Patras, Greece

    Gerasimos G. Rigatos

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  1. Gerasimos G. Rigatos
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Rigatos, G.G. (2015). Synchronization of Chaotic and Stochastic Neurons Using Differential Flatness Theory. In: Advanced Models of Neural Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43764-3_9

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  • DOI: https://doi.org/10.1007/978-3-662-43764-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43763-6

  • Online ISBN: 978-3-662-43764-3

  • eBook Packages: EngineeringEngineering (R0)

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