Universality and scaling in networks of period-doubling maps with a pacemaker.
Ivanova, Anna S., Kuznetsov, Sergey P., Osbaldestin, Andrew H. (2006)
Discrete Dynamics in Nature and Society
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Ivanova, Anna S., Kuznetsov, Sergey P., Osbaldestin, Andrew H. (2006)
Discrete Dynamics in Nature and Society
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Stefanski, Andrzej, Kapitaniak, Tomasz (2000)
Discrete Dynamics in Nature and Society
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Chen, J.Y., Wong, K.W., Zheng, H.Y., Shuai, J.W. (2002)
Discrete Dynamics in Nature and Society
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Astakhov, Vladimir, Shabunin, Alexey, Klimshin, Alexander, Anishchenko, Vadim (2002)
Discrete Dynamics in Nature and Society
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Yousefi, Shahriar, Maistrenko, Yuri, Popovych, Svitlana (2000)
Discrete Dynamics in Nature and Society
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Łukasz Korus (2011)
International Journal of Applied Mathematics and Computer Science
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The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure...
Liu, Zonghua (2010)
Mathematical Problems in Engineering
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Laugesen, J., Mosekilde, E., Bountis, T., Kuznetsov, S.P. (2000)
Discrete Dynamics in Nature and Society
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Bischi, Gian-Italo, Gardini, Laura (2000)
Discrete Dynamics in Nature and Society
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Peter E. Kloeden, Thomas Lorenz (2014)
Nonautonomous Dynamical Systems
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A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.
Al-Ola, Omar M.Abou, Fujimoto, Ken'ichi, Yoshinaga, Tetsuya (2011)
Mathematical Problems in Engineering
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Łukasz Korus (2014)
International Journal of Applied Mathematics and Computer Science
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The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical...