Transiently chaotic neural networks with piecewise linear output functions

Chaos, Solitons and Fractals

Volumn 39, Issue 2, 2009, Pages 717-730

  Chen, Shyan Shiou ^a   Shih, Chih Wen ^b  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; COMBINATORIAL OPTIMIZATION; PIECEWISE LINEAR TECHNIQUES; TRAVELING SALESMAN PROBLEM;

CHAOTIC DYNAMICS; COMBINATORIAL OPTIMIZATION PROBLEMS; ESSENTIAL DYNAMICS; OPTIMAL SOLUTIONS; PARAMETER CONDITIONS; PIECEWISE LINEAR; TRANSIENTLY CHAOTIC NEURAL NETWORKS; TRAVELLING SALESMAN PROBLEM;

NEURAL NETWORKS;

EID: 62549158682     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.01.103     Document Type: Article

References (21)

1. Hopfield J.J., and Tank D.W. Neural computation of decisions in optimization problems. Biol Cybernet 52 3 (1985) 141-152
2. Chen L., and Aihara K. Chaotic simulated annealing by neural network model with transient chaos. Neural Networks 8 6 (1995) 915-930
3. Chen L., and Aihara K. Chaos and asymptotical stability in discrete-time neural networks. Phys D 104 (1997) 286-325
4. Chen L., and Aihara K. Global searching ability of chaotic neural networks. IEEE Trans Circuits Syst I Fund Theory Appl 46 8 (1999) 974-993
5. Kwok T., and Smith K.A. A unified framework for chaotic neural network approaches to combinatorial optimization. IEEE Trans Neural Networks 10 (1999) 978-981
6. Kwok T., and Smith K.A. Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework. Neural Networks 13 (2000) 731-744
7. Tokuda I., Nagashima T., and Aihara K. Global bifurcation structure of chaotic neural networks and its application to traveling salesman problems. Neural Networks 10 (1997) 1673-1690
8. Wang L., and Smith K. On chaotic simulated annealing. IEEE Trans Neural Networks 9 (1998) 716-718
9. Blondel V.D., Bournez O., Koiran P., and Tsitsiklis N. The stability of saturated linear dynamical systems is undecidable. J Comput Syst Sci 62 (2001) 442-462
10. Chua L.O., and Yang L. Cellular neural networks: theory. IEEE Trans Circuits Syst 35 (1988) 1257-1272
11. Siegelmann H.T., and Sontage E.D. Turing computability with neural nets. Appl Math Lett 4 (1991) 77-80
12. Siegelmann H.T., and Sontage E.D. On the computational power of neural nets. J Comput Syst Sci 50 (1995) 132-150
13. Siegelmann H.T., Horne B.G., and Lee Giles C. Computational capabilities of recurrent NARX neural networks. IEEE Trans Syst Man Cybernet B 27 (1997) 208-215
14. Chen S.S., and Shih C.W. Transversal homoclinic orbits in a transiently chaotic neural network. Chaos 12 3 (2002) 654-671
15. n. J Math Anal Appl 63 (1978) 199-223
16. Marotto F.R. On redefining a snap-back repeller. Chaos, Solitons & Fractals 25 (2005) 25-28
17. Meyer K.R., and Zhang X. Stability of skew dynamical systems. J Differen Equat 132 (1996) 66-86
18. LaSalle JP. The stability of dynamical systems, ser. Regional conference series in applied mathematics, vol. 25. Philadelphia, PA: SIAM; 1976. p. 45-55.
19. Chen S.S., and Shih C.W. Asymptotic behaviors in a transiently chaotic neural network. Discr Contin Dyn Syst 10 3 (2004) 805-826
20. Chen G., Hsu S.B., and Zhou J. Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span. J Math Phys 39 12 (1998) 6459-6489
21. Li C.P., and Chen G. An improved version of the Marotto theorem. Chaos, Solitons & Fractals 18 (2003) 69-77