Search results for "Nonlinear Sciences - Chaotic Dynamics"
showing 10 items of 78 documents
Convergence of direct recursive algorithm for identification of Preisach hysteresis model with stochastic input
2015
We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive sc…
Families of piecewise linear maps with constant Lyapunov exponent
2012
We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.
Porosities and dimensions of measures
1999
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model
2005
A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pitchfork bifurcation, which preserves phase-locking, and a Hopf bifurcation, which destroys it.
A Review of Mathematical and Computational Methods in Cancer Dynamics.
2022
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the si…
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
Hidden attractors on one path : Glukhovsky-Dolzhansky, Lorenz, and Rabinovich systems
2017
In this report, by the numerical continuation method we visualize and connect hidden chaotic sets in the Glukhovsky-Dolzhansky, Lorenz and Rabinovich systems using a certain path in the parameter space of a Lorenz-like system.
Chaos in two-dimensional Kepler problem with spin-orbit coupling
2017
We consider classical two-dimensional Kepler system with spin-orbit coupling and show that at a sufficiently strong coupling it demonstrates a chaotic behavior. The chaos emerges since the spin-orbit coupling reduces the number of the integrals of motion as compared to the number of the degrees of freedom. This reduction is manifested in the equations of motion as the emergence of the anomalous velocity determined by the spin orientation. By using analytical and numerical arguments, we demonstrate that the chaotic behavior, being driven by this anomalous term, is related to the system energy dependence on the initial spin orientation. We observe the critical dependence of the dynamics on th…
Scaling behaviour of non-hyperbolic coupled map lattices
2006
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value.…
A fractal set from the binary reflected Gray code
2005
The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of $N$ the set is examined from the point of view of time series analysis