Determination of chaotic dynamic system’s paths
DOI:
https://doi.org/10.15587/2313-8416.2016.76921Keywords:
interval model, chaotic dynamics, Chua's circuit, paths, loop currentAbstract
The analysis of development methods of Chua's circuit mathematical models is done and benefits of loop currents method are substantiated. The interval mathematical model of Chua's circuit is built and its limiting attractors are defined. It is shown that the interval models usage can simultaneously examine whole possible dynamic object’s paths in a previously chosen range. The results of mathematical modeling are given
References
Tel, T., Cruiz, M. (2006). Chaotic Dynamics: An introduction based on classical mechanics. New York: Cambridge University Press, 427. doi: 10.1017/cbo9780511803277
Fortuna, L., Frasca, M., Xibilia, M. G. (2009). Chua’s circuit implementations: Yesterday, Today and Tomorrow. World Scientific Series on Nonlinear Science Series A. – Singapore: World Scientific, 224. doi: 10.1142/9789812839251
Hilborn, R. C. (2004). Chaos and nonlinear dynamics: An introduction for scientists and engineers. New York: Oxford University Press, 592.
Radwan, A. G., Soliman, A. M., El-Sedeek, A.-L. (2003). An inductorless CMOS realization of Chua’s circuit. Chaos, Solitons & Fractals, 18 (1), 149–158. doi: 10.1016/s0960-0779(02)00582-9
Moqadasi, H., Ghaznavi-Ghoushchi, M. B. (2015). A new Chua’s circuit with monolithic Chua’s diode and its use for efficient true random number generation in CMOS 180 nm. Analog Integrated Circuits and Signal Processing, 82 (3), 719–731. doi: 10.1007/s10470-015-0498-y
Yu, F., Li, P., Gu, K., Yin, B. (2016). Research progress of multi-scroll chaotic oscillators based on current-mode devices. Optik – International Journal for Light and Electron Optics, 127 (13), 5486–5490. doi: 10.1016/j.ijleo.2016.03.048
Kennedy, M. P. (1993). Three steps to chaos. II. A Chua’s circuit primer. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40 (10), 657–674. doi: 10.1109/81.246141
Matsumoto, T. (1984). A chaotic attractor from Chua’s circuit. IEEE Transactions on Circuits and Systems, 31 (12), 1055–1058. doi: 10.1109/tcs.1984.1085459
Zhong, G.-Q. (1994). Implementation of Chua’s circuit with a cubic nonlinearity. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 41 (12), 934–941. doi: 10.1109/81.340866
Bessonov, L. A. (1996). Teoreticheskie osnovy electrotehniki. Electricheskie cepi. Мoscow: Vyshaya shkola, 638.
Jaulin, L., Kieffer, M., Didrit, O., Walter, E. (2001). Applied interval analysis. London: Springer, 379. doi: 10.1007/978-1-4471-0249-6
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Copyright (c) 2016 Александр Валентинович Садовой, Роман Сергійович Волянський, Нина Викторовна Волянская
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