The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Chaotic systems are now frequently encountered in almost all branches of sciences. Dimension of such systems provides an important measure for easy characterization of dynamics of the systems. Conventional algorithms for computing dimension of such systems in higher dimensional state space face an unavoidable problem of enormous storage requirement. Here we present an algorithm, which uses a simple...
The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent...
Although plasma torches have been commercially available for about 50 years, areas such as plasma gun design, process efficiency, reproducibility, plasma stability, torch lives etc. have remained mostly unattended. Recent torch developments have been focusing on the basic understanding of the plasma column and its dynamics inside the plasma torch, the interaction of plasma jet and the powders, the...
Nuclei have complex energy-level sequence with statistical properties in agreement with canonical random matrix theory. This agreement appears when the one-particle one-hole states are mixed completely with two-particle two-hole states. In the transition, there is a new universality which we present here, bringing about a relation between dynamics and statistics. We summarize also the role of chaos...
Understanding of the basic nature of arc root fluctuation is still one of the unsolved problems in thermal arc plasma physics. It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc root behavior has been reported through the analysis of voltages, acoustic and optical signals which are generated from a hollow copper electrode arc...
The classical Duffing oscillator is a dissipative chaotic system, and so there is not a definite Hamiltonian. We quantize the Duffing oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can define a ‘Lyapunov exponent’, which corresponds to the classical one in the proper...
Transition from chaotic to ordered state has been observed during the initial stage of a discharge in a cylindrical DC glow discharge plasma. Initially it shows a chaotic behavior but increasing the discharge voltage changes the characteristics of the discharge glow and shows a period subtraction of order 7 period → 5 period → 3 period → 1 period, i.e. the system goes to single mode through odd cycle...
Bifurcations and chaos in the ubiquitous Duffing oscillator equation with different external periodic forces are studied numerically. The external periodic forces considered are sine wave, square wave, rectified since wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectangular wave with amplitude-dependent width and modulus of sine wave. Period doubling bifurcations, chaos, intermittency,...
We introduce an interesting hierarchy of rational order chaotic maps that possess an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps [1–5], with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy. We compute the Kolmogorov-Sinai entropy of these maps analytically and also their Lyapunov exponent numerically,...
A single degree-of-freedom torsional vibratory system, which constitutes a third-order dissipative dynamical system, has been fabricated as a mechanical analogue of hard Duffing equation with strong nonlinearity. The forced response of the system reveals complicated and chaotic motion at low frequency regime. Besides usual jump phenomenon, unpredictable jump phenomenon with two and three coexisting...
The equations obtained by Yang while discussing the condition of self-duality of SU(2) gauge fields on Euclidean four-dimensional space have been generalized. Exact solutions and their graphical representations for the generalized equation (for some particular values of the parameters) have been reported. They represent interesting physical characteristics like waves with spreading solitary profile,...
In the dynamic processes on networks collective effects emerge due to the couplings between nodes, where the network structure may play an important role. Interaction along many network links in the nonlinear dynamics may lead to a kind of chaotic collective behavior. Here we study two types of well-defined diffusive dynamics on scale-free trees: traffic of packets as navigated random walks, and chaotic...
The Macintosh application StdMap allows easy exploration of many of the phenomena of area-preserving mappings. This tutorial explains some of these phenomena and presents a number of simple experiments centered on the use of this program.
We study the relationship between synchronization and the rate with which information is exchanged between nodes in a spatio-temporal network that describes the dynamics of classical particles under a substrate Remoissenet-Peyrard potential. We also show how phase and complete synchronization can be detected in this network. The difficulty in detecting phase synchronization in such a network appears...
The effects of time-periodic forcing in a few-mode model for zero-Prandtl-number convection with rigid body rotation is investigated. The time-periodic modulation of the rotation rate about the vertical axis and gravity modulation are considered separately. In the presence of periodic variation of the rotation rate, the model shows modulated waves with a band of frequencies. The increase in the external...
We study the effect of parameter fluctuations and the resultant multiplicative noise on the synchronization of coupled chaotic systems. We introduce a new quantity, the fluctuation rate ϕ as the number of perturbations occurring to the parameter in unit time. It is shown that ϕ is the most significant quantity that determines the quality of synchronization. It is found that parameter fluctuations...
We introduce in this paper embedded Gaussian unitary ensemble of random matrices, for m fermions in Ω number of single particle orbits, generated by random twobody interactions that are SU(4) scalar, called EGUE(2)-SU(4). Here the SU(4) algebra corresponds to Wigner’s supermultiplet SU(4) symmetry in nuclei. Formulation based on Wigner-Racah algebra of the embedding algebra U(4Ω) ⊃ U(Ω) ⊗ SU(4) allows...
In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which an estimated critical coupling is determined. Numerical solutions are presented...
We numerically investigate the motion of a charged particle in a planetary magnetosphere using several kinds of equatorial plane phase portraits determined by two dynamical parameters: the charge-to-mass ratio and the z-component of the angular momentum. The dependence of chaos on any of the three factors including the two parameters and the energy is mainly discussed. It is found that increasing...
Our experiments with an erbium-doped fibre ring laser (CW, single transverse mode and multiaxial mode) with an intracavity LiNbO3 electro-optic modulator (EOM ) display the characteristic features of a nonlinear oscillator (e.g., harmonic and period-2 sub-harmonic resonances ) when the EOM driver voltage is modulated periodically. Harmonic resonance leads to period-1 bistability and hysteresis. Inside...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.