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Modeling chaos 1. Books: H. G. Schuster, Deterministic chaos , an introduction, VCH, 1995 H-O Peitgen, H. Jurgens, D. Saupe, Chaos and fractals Springer, 1992 H-O Peitgen, H. Jurgens, D. Saupe, Fractals for the Classroom , Part 1 and 2, Springer 1992. Journals :
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Books: H. G. Schuster, Deterministic chaos, an introduction, VCH, 1995 H-O Peitgen, H. Jurgens, D. Saupe, Chaos and fractals Springer, 1992 H-O Peitgen, H. Jurgens, D. Saupe, Fractals for the Classroom, Part 1 and 2, Springer 1992. Journals: Chaos: AnInterdisciplinaryJournalofNonlinearScience, Published by American Institute of Physics IEEE Transactions on Circuits and Systems, Published by IEEE Institute
One-dimensional discrete systems • Logistic equation • Mechanism of doubling the period • Bifurcation diagram • Doubling – period tree, Feigenbaum constants • Lyapunov exponents – chaotic solutions
Continuous-time systems • Rossler differential equation • Lorenz differential equation
Period doubling tree x r r
Why the discrete time logistic equation is so complicated compared to the continuous time one ?