Modeling chaos 1 Books H G Schuster Deterministic
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: Chaos: An Interdisciplinary Journal of Nonlinear Science, 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
One – dimensional discrete systems
Bernouli function
Triangular function
Logistic function
Sinusoidal map
Iterating logistic map
r=2. 6 x 0=0. 25
r=3. 2, x 0=0. 25
x 0=0. 25, r=3. 48
x 0=0. 2, r=4
Stability of equilibrium point:
Plot of the function: f(x)
Bifurcation diagram
Period doubling tree x r r
Why the discrete time logistic equation is so complicated compared to the continuous time one ?
- Slides: 22