Preface 1. Introduction 2. One-dimensional maps 3. Nonchaotic multidimensional flows 4. Dynamical systems theory 5. Lyapunov exponents 6. Strange attractors 7. Bifurcations 8. Hamiltonian chaos 9. Time-series properties 10. Nonlinear prediction and noise reduction 11. Fractals 12. Calculation of fractal dimension 13. Fractal measure multifractals 14. sets 15. Spatiotemporal complexity A. Common chaotic B. Useful mathematical formulas C. Journals with related papers Bibliography Index

A systematic examination of general three-dimensional autonomous ordinary differential equations with quadratic nonlinearities has uncovered 19 distinct simple examples chaotic flows either five terms and two or six one nonlinearity. The properties these systems are described, including their critical points, Lyapunov exponents, fractal dimensions.

Using the Routh–Hurwitz stability criterion and a systematic computer search, 23 simple chaotic flows with quadratic nonlinearities were found that have unusual feature of having coexisting stable equilibrium point. Such systems belong to newly introduced category hidden attractors are important potentially problematic in engineering applications.

A new simple four-dimensional equilibrium-free autonomous ODE system is described. The has seven terms, two quadratic nonlinearities, and only parameters. Its Jacobian matrix everywhere rank less than 4. It hyperchaotic in some regions of parameter space, while other it an attracting torus that coexists with either a symmetric pair strange attractors or limit cycles whose basin boundaries have intricate fractal structure. In three coexisting Arnold tongues. Since there are no equilibria, all...

With the abundance of chaotic systems that have now been identified and studied, it is prudent to establish a standard for publication new examples such develop acceptable criteria their characterization.

In this paper, we describe a periodically-forced oscillator with spatially-periodic damping. This system has an infinite number of coexisting nested attractors, including limit cycles, attracting tori, and strange attractors. We are aware no similar example in the literature.

Multistability exists in various regimes of dynamical systems and different combinations, among which there is a special one generated by self-reproduction. In this paper, we describe method for constructing self-reproducing from unique class variable-boostable whose coexisting attractors reside the phase space along specific coordinate axis any can be selected choosing an initial condition its corresponding basin attraction.

Many new chaotic systems with algebraically simple representations are described. These involve a single third-order autonomous ordinary differential equation (jerk equation) various nonlinearities. Piecewise linear functions emphasized to permit easy electronic implementation diodes and operational amplifiers. Several robust electrical circuits described evaluated.

A numerical examination of third-order, one-dimensional, autonomous, ordinary differential equations with quadratic and cubic nonlinearities has uncovered a number algebraically simple involving time-dependent accelerations (jerks) that have chaotic solutions. Properties some these systems are described, suggestions given for further study.

The Madison Symmetric Torus (MST) is the newest and largest reversed-field pinch (RFP) currently in operation. It incorporates a number of design features that set it apart from other pinches, including use conducting shell as both vacuum vessel single-turn toroidal field coil. Specially insulated voltage gaps are exposed to plasma. Magnetic errors at these well various diagnostic pumping ports minimized through variety techniques. physics goals MST include study effect large plasma size on...

Much recent interest has been given to simple chaotic oscillators based on jerk equations that involve a third-time derivative of single scalar variable. The simplest such equation yet be electronically implemented. This paper describes particularly elegant circuit whose operation is accurately described by variant in which the requisite nonlinearity provided diode and for analysis straightforward.

In this paper, the dynamical behavior of Lorenz system is examined in a previously unexplored region parameter space, particular, where r zero and b negative. For certain values parameters, classic butterfly attractor broken into symmetric pair strange attractors, or it shrinks small basin intermingled with basins limit cycles, which means that bistable tristable under conditions. Although resulting no longer plausible model fluid convection, may have application to other physical systems.

For a dynamical system described by set of autonomous ordinary differential equations, an attractor can be point, periodic cycle, or even strange attractor. Recently, new chaotic with only one stable equilibrium was described, which locally converges to the but is globally chaotic. This paper further shows that for certain parameters, besides point and attractor, this also has coexisting limit demonstrating truly complicated interesting.

We report on the finding of hidden hyperchaos in a 5D extension to known 3D self-exciting homopolar disc dynamo. The is identified through three positive Lyapunov exponents under condition that proposed model has just two stable equilibrium states certain regions parameter space. new hyperchaotic dynamo multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, chaos or hyperchaos, as well coexisting attractors. use numerical integrations create phase plane...