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Application of Local Activity Theory of CNN to the Coupled Autocatalator Model

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7951)

Abstract

The study of chemical reactions with oscillating kinetics has drawn increasing interest over the last few decades. However the dynamical properties of the coupled nonlinear dynamic system are difficult to deal with. The local activity principle of the Cellular Nonlinear Network (CNN) introduced by Chua has provided a powerful tool for studying the emergence of complex behaviors in a homogeneous lattice formed by coupled cells. Based on the Autocatalator Model introduced by Peng.B, this paper establishes a two dimensional coupled Autocatalator CNN system. Using the analytical criteria for the local activity calculates the chaos edge of the Autocatalator CNN system. The numerical simulations show that the emergence may exist if the selected cell parameters are nearby the edge of chaos domain. The Autocatalator CNN can exhibit periodicity and chaos.

Keywords

  • Cellular Nonlinear Network
  • edge of chaos
  • reaction diffusion equation
  • chaos

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Wen, G., Meng, Y., Min, L., Zhang, J. (2013). Application of Local Activity Theory of CNN to the Coupled Autocatalator Model. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-39065-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39064-7

  • Online ISBN: 978-3-642-39065-4

  • eBook Packages: Computer ScienceComputer Science (R0)