By building the complete bifurcation diagrams with stable and unstable periodic solutions, we have found different new bifurcation groups with their own rare regular and chaotic attractors.
Our aim was to build complete bifurcation diagrams and to find new bifurcation groups and unknown rare regular and chaotic attractors using complete bifurcation analysis in these pendulum systems.
Given that such sporadic shocks are not uncommon in foreign exchange markets, a grandiose aspiration of finding a long-term steady-state dynamical path by locating a chaotic attractor would be impractical.
1990] do not examine the R/S analysis, (perhaps because the R/S analysis was not popular in the study of economic data sets before Peters ), it does not claim to locate a chaotic attractor either.
In fact, chaotic attractors are complex but subtly ordered structures; they are manifestations of what can better be described as structured disorder.
In addition, recent research (McGlade 1990; 1993; in press) has indicated the likely presence of chaotic attractors within unstable regimes such as are represented by prehistoric trade/exchange dynamics.
In the context of your discussion of chaotic attractors and openended systems, you said that humans were also part of an open system.
This is one of the simplest chaotic attractors we know.
Among the topics are symmetrical multi-petal chaotic attractors
in a three-dimensional autonomous system with only one stable equilibrium, catastrophic bifurcation in three-phase voltage-source converters, a chaotic image encryption scheme based on magic cube transformations, the global synchronization of a hyperchaotic system with four wings, and generating multi-scroll attractors from fractal and multi-fractal processes.
of Johannesburg) has updated his material to reflect advances in technique as well as research, and to give students insights into how they will be expected to apply these techniques and concepts in real life, where chaotic attractors
are using neural networks, fractals are used in data compression, and neural networks and fuzzy logic are combined.
The nonlinear workbook; chaos, fractals, cellular automata, neural networks, genetic algorithms, gene expression programming, support vector machine, wavelets, hidden Markov models, fuzzy logic..., 4th ed
These processes build up structures we use to classify chaotic systems that are fractals and the unstable periodic orbits that exist in chaotic attractors