sciences exist to demonstrate the fundamental order underlying nature. chaos/complexity theory is a novel and amazing field of scientific inquiry. notions of our everyday experiences are somehow in connection to the laws of nature through chaos/complexity theory’s concerns with the relationships between simplicity and complexity, between orderliness and randomness (retrieved from http://www.inc...

Introduction: Based on Voyager imaging of Jupiter’s moon Europa, Lucchita and Soderblom [1] classified the surface of this icy satellite into two major terrain types: plains and mottled terrain. Mottled terrain was defined as consisting of isolated small spots, hummocky topography, and sometimes broken-up lineae. One of the primary goals of the Galileo mission was to determine the origin and pa...

– In this paper the attention is focused on the chaotic dynamics of a new circuit driven by two sinusoidal signals. In particular, it is illustrated that the application of signals with slightly different frequencies enables the novel phenomenon of chaotic beats to be generated. Moreover, the paper shows that the proposed circuit can be considered the simplest nonautonomous circuit able to gene...

Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the simulation, parameter estimation, and control of mechanical sys...

We show experimentally that two coupled chaotic systems initially operating on two different simultaneously co-existing attractors can be synchronized. Synchronization is achieved as one of the systems switches its evolution to the attractor of the other one. The final attractor of the synchronized state strongly depends on the actual position of trajectories on their attractors at the moment w...

This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov’s stability theo...

A numerical behavior of a KdV combined mKdV equation is obtained using the Melnikov method. Melnikov method is proved to be elegant, and successful alternative to characterizing the complex dynamics of multi-stable oscillators. Based on the Melnikov theory we present the homoclinic and heteroclinic orbits in the unperturbed system. It is show us whether the system is chaotic or not. In this wor...

In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lü et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical e...

Fractional-order financial system introduced by W.-C. Chen 2008 displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreove...

In this paper the method of critical curves, a tool for the study of the global dynamical properties of two-dimensional noninvertible maps, is applied to the study of chaos synchronization and related phenomena of riddling, blowout, and on-off intermittency. A general procedure is suggested in order to obtain the boundary of a particular two-dimensional compact trapping region, called absorbing...