Parameters identification of chaotic systems via chaotic ant swarm. (English) Zbl 1121.90426

Li, Lixiang; Yang, Yixian; Peng, Haipeng; Wang, Xiangdong

Chaos Solitons Fractals 28, No. 5, 1204-1211 (2006).

Summary: Through the construction of a suitable fitness function, the problem of parameters estimation of the chaotic system is converted to that of parameters optimization. In this paper, an optimization method, called CAS (chaotic ant swarm), is developed to solve the problem of searching for the optimal. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed method.

MSC:

90C59	Approximation methods and heuristics in mathematical programming
37N35	Dynamical systems in control
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93E11	Filtering in stochastic control theory

References:

[1]	Aihara, K.; Takabe, T.; Toyoda, M., Chaotic neural networks, Phys Lett A, 144, 333-340 (1990)
[2]	Chen, L.; Aihara, K., Chaotic simulated annealing by a neural network model with transient chaos, Neural Networks, 8, 915-930 (1995)
[3]	Hasegawa, M.; Ikeguchi, T.; Aihara, K.; Itoh, K., A novel chaotic search for quadratic assignment problems, Eur J Operat Res, 139, 543-556 (2002) · Zbl 0995.90059
[4]	Li, B.; Jiang, W., Optimizing complex functions by chaos search, Int J Cybernet Syst, 29, 409-419 (1998) · Zbl 1012.90068
[5]	Hayakawa, Y.; Marumoto, A.; Sawada, Y., Effects of the chaotic noise on the performance of a neural network model for optimization problems, Phys Rev E, 51, 2693-2696 (1995)
[6]	Annan, J. D.; Hargreaves, J. C., Efficient parameter estimation for a highly chaotic system, Tellus, 56A, 520-526 (2004)
[7]	Parlitz, U., Estimating model parameters from time series by autosynchronization, Phys Rev Lett, 76, 1232-1235 (1996)
[8]	Chen, S. H.; Hu, J.; Wang, C. H.; Lü, J. H., Adaptive synchronization of uncertain Rössler hyperchaotic system based on parameter identification, Phys Lett A, 321, 50-55 (2004) · Zbl 1118.81326
[9]	Li, L. X.; Peng, H. P.; Wang, X. D.; Yang, Y. X., Comment on two papers of chaotic synchronization, Phys Lett A, 333, 269-270 (2004) · Zbl 1123.37324
[10]	Guan, X. P.; Peng, H. P.; Li, L. X.; Wang, Y. Q., Parameter identification and control of Lorenz system, Acta Phys Sin, 50, 26-29 (2001), [in Chinese]
[11]	Lü, J. H.; Zhang, S. H., Controlling Chen’s chaotic attractor using backstepping design based on parameters identification, Phys Lett A, 286, 148-152 (2001) · Zbl 0969.37509
[12]	Lie, J.; Chen, S.; Xie, J., Parameter identification and control of uncertain unified chaotic system via adaptive extending equilibrium manifold approach, Chaos, Solitons & Fractals, 19, 533-540 (2004) · Zbl 1085.93524
[13]	Gu, M.; Kalaba, R. E.; Taylor, G. A., Obtaining initial parameter estimates for chaotic dynamical systems using linear associative memories, Appl Math Comput, 76, 143-159 (1996) · Zbl 0846.65030
[14]	Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G., Cryptanalysis of an ergodic chaotic cipher, Phys Lett A, 311, 172-181 (2003) · Zbl 1027.94009
[15]	Wu, X.; Hu, H.; Zhang, B., Parameter estimation only from the symbolic sequences generated by chaos system, Chaos, Solitons & Fractals, 22, 359-366 (2004) · Zbl 1061.94043
[16]	Monmarché, N.; Veturini, G.; Slimane, M., On how Pachycondyla apicalis ants suggests a new search algorithm, Future Generat Comput Syst, 16, 937-946 (2000)
[17]	Cole, B. J., Is animal behavior chaotic? evidence from the activity of ants, Proc Roy Soc Lond, Series B-Biol Sci, 244, 253-259 (1991)
[18]	Solé, R. V.; Miramontes, O.; Goodwill, B. C., Oscillations and chaos in ant societies, J Theor Biol, 161, 343-357 (1993)
[19]	Seifritz, W., Functional logitstic mapping, Chaos, Solitons & Fractals, 7, 1417-1425 (1996) · Zbl 1080.37507
[20]	Zhou, T.; Chen, G.; Tang, Y., A universal unfolding of the Lorenz system, Chaos, Solitons & Fractals, 20, 979-993 (2004) · Zbl 1048.37032