A new chaotic Hopfield neural network and its synthesis via parameter switchings

Neurocomputing

Volumn 117, Issue , 2013, Pages 33-39

  Li, Juan ^a   Liu, Feng ^a   Guan, Zhi Hong ^a   Li, Tao ^b  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b YANGTZE UNIVERSITY   (China)

Author keywords

Hopfield neural networks; Horseshoe; New chaos; Parameter switching; Synthesis of chaos

Indexed keywords

CHAOTIC ATTRACTORS; CHAOTIC HOPFIELD NEURAL NETWORKS; HORSESHOE; NUMERICAL EXAMPLE; NUMERICAL EXPERIMENTS; PARAMETER SWITCHING; TOPOLOGICAL ENTROPY; TOPOLOGICAL HORSESHOES;

CHAOS THEORY; NEURAL NETWORKS; TOPOLOGY;

HOPFIELD NEURAL NETWORKS;

ACCURACY; ALGORITHM; ARTICLE; CALCULATION; ENTROPY; HISTOGRAM; HOPFIELD NEURAL NETWORK; MACHINE LEARNING; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONLINEAR SYSTEM; PRIORITY JOURNAL; RELIABILITY; UNCERTAINTY;

EID: 84878924304     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.11.022     Document Type: Article

References (35)

1. Huang Y., Yang X.-S. Hyperchaos and bifurcation in a new class of four-dimensional Hopfield neural networks. Neurocomputing 2006, 69:1787-1795.
2. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 1984, 81:3088-3092.
3. Guan Z.-H., Chen G. On delayed impulsive Hopfield neural network. Neural Networks 1999, 12:273-280.
4. Guan Z.-H., Chen G., Qin Y. On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans. Neural Networks 2000, 11:534-540.
5. Guan Z.-H., James L., Chen G. On impulsive auto-associative neural networks. Neural Networks 2000, 13:63-69.
6. Babloyantz A., Lourenco C. Brain chaos and computation. Int. J. Neural Syst. 1996, 7:461-471.
7. Dror G., Tsodyks M. Chaos in neural networks with dynamic synapses. Neurocomputing 2000, 32-33:365-370.
8. He G., Chen L., Aihara K. Associative memory with a controlled chaotic neural network. Neurocomputing 2008, 71:2794-2805.
9. Li Q., Yang X.-S., Yang F. Hyperchaos in Hopfield-type neural networks. Neurocomputing 2005, 67:275-280.
10. Huang W., Huang Y. Chaos of a new class of Hopfield neural networks. Appl. Math. Comput. 2008, 206:1-11.
11. Yang X.-S., Yuan Q. Chaos and transient chaos in simple Hopfield neural networks. Neurocomputing 2005, 69:232-241.
12. Yang X.-S., Li Q., Cheng S. Horseshoe chaos and topological entropy estimate in a simple power system. Appl. Math. Comput. 2009, 211:467-473.
13. Zheng P., Tang W., Zhang J. Some novel double-scroll chaotic attractors in Hopfield networks. Neurocomputing 2010, 73:2280-2285.
14. Yang X.-S., Huang Y. A new class of chaotic simple 3-cell cellular neural network. Int. J. Bifurcation Chaos 2006, 16:1019-1021.
15. Yuan Q., Li Q., Yang X.-S. Horseshoe chaos in a class of simple Hopfield neural networks. Chaos Solitons Fractals 2009, 39:1522-1529.
16. Lorenz E.N. Deterministic Nonperiodic Flow. J. Atmos. Sci. 1963, 20:130-141.
17. Chen G., Ueta T. Yet another chaotic attractor. Int. J. Bifurcation Chaos 1999, 9:1465-1466.
18. Liu C., Liu T., Liu L., Liu K. A new chaotic attractor. Chaos, Solitons Fractals 2004, 22:1031-1038.
19. Upadhyay R.K., Rai V. Why chaos is rarely observed in natural populations. Chaos Solitons Fractals 1997, 12:1933-1939.
20. Chen G., Shi Y.M. Introduction to anti-control of discrete chaos. theory and applications. Phil. Trans. R. Soc. A 2006, 364:2433-2447.
21. Guan Z.-H., Liu N. Generating chaos for discrete time-delayed systems via impulsive control. Chaos 2010, 20:013135.
22. Guan Z.-H., Liu F. Chaotification of complex networks with impulsive control. Chaos 2012, 22:023137.
23. Liu N., Guan Z.-H. The chaotification of discrete Hopfield neural networks via impulsive control. Chin. Phys. Lett. 2009, 26:070503.
24. Liu N., Guan Z.-H. Chaotification of discrete dynamical systems via impulsive control. Phys. Lett. A 2009, 373:2131-2136.
25. Danca M.-F. Synthesizing the Lü attractor by parameter-switching. Int. J. Bifurcation Chaos 2011, 21:323-331.
26. Danca M.-F. Attractors synthesis for a Lotka-Volterra like system. Appl. Math. Comput. 2010, 216:2107-2117.
27. Yang X.-S., Tang Y. Horseshoes in piecewise continuous maps. Chaos Solitons Fractals 2004, 19:841-845.
28. Robinson R.C., Robinson C. Dynamical Systems. Stability, Symbolic Dynamics, and Chaos 1999, CRC Press.
29. Li Q., Yang X.-S. New walking dynamics in the simplest passive bipedal walking model. Appl. Math. Modelling 2012, 36:5262-5271.
30. Li Q., Yang X.-S. A simple method for finding topological horseshoes. Int. J. Bifurcation Chaos 2010, 20:467-478.
31. Danca M.-F., Tang W.K.S., Chen G. A switching scheme for synthesizing attractors of dissipative chaotic systems. Appl. Math. Comput. 2008, 201:650-667.
32. Danca M.-F. Random parameter-switching synthesis of a class of hyperbolic attractors. Chaos 2008, 18:33111.
33. Danca M.-F., Diethelm K. Fractional-order attractors synthesis via parameter switchings. Commun. Nonlinear Sci. Numer. Simulat. 2010, 15:3745-3753.
34. Danca M.-F., Romera M., Pastor G., Montoya F. Finding attractors of continuous-time systems by parameter switching. Nonlinear Dyn. 2012, 67:2317-2342.
35. Sánchez-López C. Automatic synthesis of chaotic attractors. Appl. Math. Comput. 2011, 217:4350-4358.