Skip to main content
SpringerLink
Log in

Chaotic neural network controlled by particle swarm with decaying chaotic inertia weight for pattern recognition

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This study introduces a new type of chaotic neural network, which is built upon perturbed Duffing oscillator. The neurons in this network behave collectively based on a modified version of Duffing map. The proposed neural processor can act chaotically at some areas of the state space. The network has some parameters, which can be adjusted for the system to behave either chaotically or periodically. This nonlinear network adopts the bifurcating behavior of the chaotic Duffing map for the most covered search in the neuronal search space. The neuron’s search space is controlled by swarming in the parameter space to settle the parameters of the network into the critical parameters. Swarming of the parameters is based on particle swarm optimization heuristic. The modified particle swarm adopts a decaying inertia weight based on chaotic logistic map to fast settle down into the attractors of periodic solutions. At last, the swarm-controlled neurochaotic processor is applied to build three models to control parameters of the network. Each model is trained to recognize a set of binary patterns that are as the form of alphabetic letters as a classical pattern recognition problem. A comparison study is then conducted among these three models, Hopfield network and a modified Hopfield model, which demonstrate all three models outperform Hopfiled model and are competitive and in most cases outperform the modified Hopfield model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Babloyantz A, Destexhe A (1986) Low-dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA 83:3513–3517

    Article  Google Scholar 

  2. Aradi I, Barna G, Erdi P, Grobler T (1995) Chaos and learning in the olfactory bulb. Int J Intell Syst 10:89–117

    Article  MATH  Google Scholar 

  3. Baird B (1986) Nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb. Physica D 22:150–175

    Article  MathSciNet  Google Scholar 

  4. Freeman WJ (1991) The physiology of perception. Sci Am 264(2):78–85

    Article  MathSciNet  Google Scholar 

  5. Freeman WJ (1992) Tutorial on neurobiology: from single neurons to brain chaos. Int J Bifurcat Chaos 2:451–482

    Article  MATH  Google Scholar 

  6. Guevara MR, Glass L, Mackey MC, Shrier A (1983) Chaos in neurobiology. IEEE Trans Syst Man Cybern 13:790–798

    MATH  Google Scholar 

  7. Kurten KE, Clark JW (1986) Chaos in neural systems. Phys Lett A 114:413–418

    Article  MathSciNet  Google Scholar 

  8. Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161–165

    Article  Google Scholar 

  9. Freeman WJ, Yao Y, Burke B (1988) Central pattern generating and recognizing in olfactory bulb: a correlation learning rule. Neural Netw 1:277–288

    Article  Google Scholar 

  10. Birbaumer N, Lutzenberger W, Rau H, Braun C, Mayer-Kress G (1996) Perception of music and dimensional complexity of brain activity. Int J Bifurcat Chaos 6:267–278

    Article  Google Scholar 

  11. Chay TR, Fan YS (1995) Bursting, spiking, chaos, fractal, and universality in biological rhythms. Int J Bifurcat Chaos 5:595–635

    Article  MATH  Google Scholar 

  12. Fuchs A, Kelso JAS, Haken H (1992) Phase transition in human brain: spatial mode dynamics. Int J Bifurcat Chaos 2:917–939

    Article  MATH  Google Scholar 

  13. Liebovitch LS, Czegledy FP (1991) A model of ion channel kinetics based on deterministic chaotic motion in a potential with two local minima. Ann Biomed Eng 20:517–531

    Article  Google Scholar 

  14. Freeman WJ (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biol Cybern 56:139–150

    Article  Google Scholar 

  15. Yao Y, Freeman WJ (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Netw 3:153–170

    Article  Google Scholar 

  16. Chang-song Z, Tian-lin C, Wu-qun H (1997) Chaotic neural network with nonlinear self-feedback and its application in optimization. Neurocomputing 14:209–222

    Article  Google Scholar 

  17. Chen L, Aihara K (1995) Chaotic simulated annealing by a neural network model with transient chaos. Neural Netw 8:915–930

    Article  Google Scholar 

  18. Adachi M, Aihara K (1997) Associative dynamics in a chaotic neural network. Neural Netw 10:83–98

    Article  Google Scholar 

  19. Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 144:333–340

    Article  MathSciNet  Google Scholar 

  20. Albers DJ, Sprott JC, Dechert WD (1998) Routes to chaos in neural networks with random weight. Int J Bifurcat Chaos 8:1463–1478

    Article  MATH  Google Scholar 

  21. Kaneko K (1990) Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements. Physica D 41:137–172

    Article  MATH  MathSciNet  Google Scholar 

  22. Andreyev YV, Dmitriev AS, Starkov SO (1997) Information processing in 1-D systems with chaos. IEEE Trans Circuits Syst 44:21–28

    Article  Google Scholar 

  23. Dmitriev AS, Kuminov DA (1994) Chaotic scanning and recognition of images in neuron-like systems with learning. J Commun Tech Electron 39:118–127

    Google Scholar 

  24. Grossberg S (1988) Nonlinear neural networks: principles, mechanisms, and architectures. Neural Netw 1:17–61

    Article  Google Scholar 

  25. Hayakawa Y, Marumoto A, Sawada Y (1995) Effects of the chaotic noise on the performance of a neural network model for optimization problems. Phys Rev E 51:R2693–R2696

    Article  Google Scholar 

  26. Ishii S, Fukumizu K, Watanabe S (1996) A network of chaotic elements for information processing. Neural Netw 9:25–40

    Article  Google Scholar 

  27. Kwok T, Smith KA (1999) A unified framework for chaotic neural network approach to combinatorial optimization. IEEE Trans Neural Netw 10:978–981

    Article  Google Scholar 

  28. Zak M (1989) Terminal attractors in neural networks. Neural Netw 2:259–274

    Article  Google Scholar 

  29. Nakagawa M (1999) A chaos associative model with a sinusoidal activation function. Chaos Solitons Fractals 10:1437–1452

    Article  MATH  Google Scholar 

  30. Potapov AB, Ali MK (2000) Robust chaos in neural networks. Phys Lett A 277:310–322

    Article  MATH  MathSciNet  Google Scholar 

  31. Tan Z, Ali MK (1998) Pattern recognition in a neural network with chaos. Phys Rev E 58:3649–3653

    Article  Google Scholar 

  32. Tan Z, Ali MK (2001) Associative memory using synchronization in a chaotic neural network. Int J Modern Phys C 12:19–29

    Article  Google Scholar 

  33. Tan Z, Hepburn BS, Tucker C, Ali MK (1998) Pattern recognition using chaotic neural networks. Discrete Dyn Nature Soc 2:243–247

    Article  MATH  Google Scholar 

  34. Tsuda I (1992) Dynamic link of memory–chaotic memory map in nonequilibrium neural networks. Neural Netw 5:13–326

    Article  Google Scholar 

  35. Hiura E, Tanaka T (2007) A chaotic neural network with duffing’s equation. In: Proceedings of international joint conference on neural networks, Orlando, pp 997–1001

  36. Song Y, Chen ZQ, Yuan ZZ (2007) New chaotic PSO-based neural network predictive control for nonlinear process. IEEE Trans Neural Netw 18:595–600

    Article  Google Scholar 

  37. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79:2554–2558

    Article  MathSciNet  Google Scholar 

  38. Parker TS, Chua LO (1987) Chaos: a tutorial for engineers. In: Proceedings of the IEEE special issue on chaotic systems, pp 982–1008

  39. Yang J, Qu Z, Hu G (1996) Duffing equation with two periodic forcings: the phase effect. Physical Rev E 53(5):4402–4413

    Article  MathSciNet  Google Scholar 

  40. Daneshyari M (2008) A neurochaotic PSO-guided network based upon perturbed duffing oscillator. In: Proceedings of international joint conference on neural networks, Hong Kong, pp 2315–2320

  41. Yen GG, Daneshyari M (2006) Diversity-based information exchange among multiple swarms in particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation, Vancouver, pp 1686–1693

  42. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of international joint conference on neural networks, Perth, pp 1942–1948

  43. Daneshyari M, Yen GG (2008) Cultural MOPSO: a cultural framework to adapt parameters of multiobjective particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation, Hong Kong, pp 1325–1332

  44. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE international conference on evolutionary computation, pp 69–73

  45. Banks A, Vincent J, Anyakoha C (2007) A review of particle swarm optimization, part I: background and development. Nat Comput 6(4):467–484

    Article  MATH  MathSciNet  Google Scholar 

  46. Hu CLJ (2003) Design and noniterative learning of multiple pattern storage in a modified hopfield net. In: Proceedings of SPIE, vol 5106, pp 154–160

  47. Fogel DB, Fogel LJ, Atmar JW (1991) Meta-evolutionary programming. In: Proceedings of the 25th asilomar conference on signals, systems and computers, Pacific Grove, California, pp 540–545

Download references

Author information

Authors and Affiliations

  1. Department of Technology, Elizabeth City State University, Elizabeth City, NC, 27909, USA

    Moayed Daneshyari

  2. Department of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK, 74078, USA

    Moayed Daneshyari

Authors
  1. Moayed Daneshyari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moayed Daneshyari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Daneshyari, M. Chaotic neural network controlled by particle swarm with decaying chaotic inertia weight for pattern recognition. Neural Comput & Applic 19, 637–645 (2010). https://doi.org/10.1007/s00521-009-0322-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-009-0322-7

Keywords

Search

Navigation