Call for Paper - March 2023 Edition
IJCA solicits original research papers for the March 2023 Edition. Last date of manuscript submission is February 20, 2023. Read More

Investigation of a Chaotic Spiking Neuron Model

Print
PDF
International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 99 - Number 17
Year of Publication: 2014
Authors:
M. Alhawarat
T. Olde Scheper
N. T. Crook
10.5120/17462-8258

M Alhawarat, Olde T Scheper and N T Crook. Article: Investigation of a Chaotic Spiking Neuron Model. International Journal of Computer Applications 99(17):1-8, August 2014. Full text available. BibTeX

@article{key:article,
	author = {M. Alhawarat and T. Olde Scheper and N. T. Crook},
	title = {Article: Investigation of a Chaotic Spiking Neuron Model},
	journal = {International Journal of Computer Applications},
	year = {2014},
	volume = {99},
	number = {17},
	pages = {1-8},
	month = {August},
	note = {Full text available}
}

Abstract

Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to exploit such properties. In this paper, a chaotic spiking neuron model is investigated experimentally. This investigation is performed to understand the dynamic behaviours of the model. The aim of this research is to investigate the dynamics of the nonlinear dynamic state neuron (NDS) experimentally. The experimental approach has revealed some quantitative and qualitative properties of the NDS model such as the control mechanism, the reset mechanism, and the way the model may exhibit dynamic behaviours in phase space. It is shown experimentally in this paper that both the reset mechanism and the self-feed back control mechanism are important for the NDS model to work and to stabilise to one of the large number of available unstable periodic orbits (UPOs) that are embedded in its attractor. The experimental investigation suggests that the internal dynamics of the NDS neuron provide a rich set of dynamic behaviours that can be controlled and stabilised. These wide range of dynamic behaviours may be exploited to carry out information processing tasks.

References

  • M. O. I. Alhawarat. Learning and Memory in Chaotic Spiking Neural Models. PhD thesis, Oxford Brookes University, 2007.
  • MarioAntoine Aoun. Stdp within nds neurons. In Advances in Neural Networks - ISNN 2010, volume 6063 of Lecture Notes in Computer Science, pages 33–43. Springer Berlin Heidelberg, 2010.
  • A. Babloyantz and C. Lourenc¸o. Brain chaos and computation. International Journal of Neural Systems, 7:461–471, 1996.
  • A. Bershadskii and Y. Ikegaya. Chaotic neuron clock. Chaos, Solitons & Fractals, 44(45):342 – 347, 2011.
  • Nigel Crook and Wee Jin Goh. Nonlinear transient computation as a potential "kernel trick" in cortical processing. Biosystems, 94(1-2):55–59, 2008.
  • N. T. Crook, W. J. Goh, and M. Hawarat. Pattern recall in networks of chaotic neurons. BioSystems, 87:267–274, 2007.
  • N. T. Crook, W. J. Goh, and M. O. Hawarat. The nonlinear dynamic state neuron. In M. Verleysen, editor, ESANN, pages 37–42, Bruges, Belgium, April 2005. 13th European Symposium on Artificial Neural Networks (ESANN'2005).
  • N. T. Crook, T. V. S. M. olde Scheper, and V. Pathirana. Self organised dynamic recognition states for chaotic neural networks. Information Sciences, 150(1-2):59–75, March 2003.
  • Alain Destexhe. Oscillations, complex spatiotemporal behavior, and information transport in networks of excitatory and inhibitory neurons. Physical Review E, 50(2):1594–1606, Aug 1994.
  • H. G. Schuster (ed. ), editor. Handbook of Chaos Control. Wiley-VCH Verlag GmbH, 1999.
  • A. Fourati, M. Feki, and N. Derbel. Stabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller. Nonlinear Dynamics, 62:687–704, 2010.
  • G. W. Frank, T. Lookman, M. A. H. Nerenberg C. Essex, J. Lemieux, and W. Blume. Chaotic time series analyses of epileptic seizures. Physica D, 46:427–438, 1990.
  • S. Scarda W. J. Freeman. How brains make chaos in order to make sense of the world. Brain and Behavioral Science, 10:161–195, November 1987.
  • W. J. Freeman. Strange attractors in the olfactory system of rabbits. Electroencephalography and Clinical Neurophysiology, 61(S155–S155):139–150, 1985.
  • W. J. Freeman. A proposed name for aperiodic brain activity: stochastic chaos. Neural Networks, 13(1):11–13, 2000.
  • W. J. Freeman and J. M. Barrie. Chaotic oscillations and the genesis of meaning in cerebral cortex. Temporal Coding in the Brain, pages 13–37, 1994.
  • W. J Goh and N. T. Crook. Pattern recognition using chaotic transients. In 15th European Symposium on Artificial Neural Networks (ESANN-2007), pages 7–12, April 2007.
  • E. Ott, C. Grebogi, and J. A. Yorke. Controlling chaos. Physical Review Letters, 64:1196–1199, 1990.
  • F. Pasemann and N. Stollenwerk. Attractor switching by neural control of chaotic neurodynamics. Network: Computational Neural Systems, 9(4):549–561, November 1998.
  • V. Piccirillo, J. M. Balthazar, B. R. Pontes, and J. L. P. Felix. Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part i: Ideal energy source. Nonlinear Dynamics, 55:139–149, 2009.
  • K. Pyragas. Continuous control of chaos, by self-controlling feedback. Physics Letters A, 170:421–428, 1992.
  • O. E. R¨ossler. An equation for continuous chaos. Physics Letters A, 57(5):397–398, 1976.
  • J. Theiler. On the evidence for low-dimensional chaos in an epileptic electroencephalogram. Physics Letters A, 196:335–341, 1995.
  • Hua Wang, Zhengzhi Han, Qiyue Xie, and Wei Zhang. Finite-time chaos control of unified chaotic systems with uncertain parameters. Nonlinear Dynamics, 55:323–328, 2009.
  • Yu-Te Wu, Kuo-Kai Shyu, Tzong-Rong Chen, and Wan-Yuo Guo. Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images. Nonlinear Dynamics, 58:745–752, 2009.