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The basic dynamic properties of a four dimensional hyperchaotic system are investigated in this paper. More precisely, the stability of equilibrium point of hyperchaotic system is studied by means of nonlinear dynamics theory. We analyses the existence and stability of Hopf bifurcation, and the formulas for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. In addition, a sliding mode controller is designed and controlled the hyperchaotic system to any fixed point to eliminate the chaotic vibration by means of sliding mode method. Finally, the numerical simulations were presented to confirm the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the problem of controlling chaos in a 3D ratio-dependent food chain system. Time-delayed feedback control method is applied to suppress chaos to unstable equilibria or unstable periodic orbits. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Some numerical simulations are presented to support theoretical predictions. Finally, main conclusions are drawn. [ABSTRACT FROM AUTHOR]

Based on a very special property of the shift map (Theorem 1), we believe that chaos should involve not only nearby points can diverge apart but also far apart points can get close to each other and these happen infinitely often. Therefore, we propose to call a continuous map f(x) from an infinite compact metric space (G, d) (with metric d) to itself chaotic if there exists a positive number δ such that for any point x and any nonempty open set V (not necessarily an open neighborhood of x) in G there is a point y in V such that limsupn→∞ d(fn(x), fn(y)) ≥ δ and liminfn→∞ d(fn(x), fn(y)) = 0. [ABSTRACT FROM AUTHOR]

Researchers are finding their way to solve the chaotic and uncertain problems using the extensions of classical fuzzy model. At present Interval Type-2 Fuzzy logic Systems (IT2-FLS) are extensively used after the thriving exploitation of Type-2 FLS. Fuzzy time series models have been used for forecasting stock and FOREX indexes, enrollments, temperature, disease diagnosing and weather. In this paper an integrated fuzzy time series model based on ARIMA and IT2-FLS is presented. The propose model will use ARIMA to select appropriate coefficients from the observed dataset. IT2-FLS is utilized here for forecasting the result with more accuracy and certainty. [ABSTRACT FROM AUTHOR]

This paper presents the study of the axial dual-spin spacecraft dynamics. These spacecraft are usually called gyrostats. The gyrostat is composed of two rigid bodies: an asymmetric platform and an axisymmetric rotor aligned with the platform principal axis. The dynamics of gyrostats without external torque is considered. The dynamics is described by using ordinary differential equations with Andoyer-Deprit canonical variables. For undisturbed motion, when the internal torque is equal to zero and the moments of inertia of the gyrostat are constant, the stationary solutions are found, and their stability is studied. Also we obtain general exact analytical solutions in terms of elliptic functions. These results can be interpreted as the development of the classical Euler case for a solid with additional degree of freedom - the relative rotation of bodies. Results of the study can be useful for the analysis of dual-spin spacecraft dynamics and for studying the chaotic behavior of the spacecraft. [ABSTRACT FROM AUTHOR]

This paper proposes a robust suppression sliding mode controller design for uncertain Duffing-Holmes chaotic systems. A form of time-varying second-order differential equation is organized to describe the dynamical system. Control system performance is proved robust against parametric uncertainties and external disturbances. The control input involves a discontinuous switching control input which is used to deal with the uncertainties and disturbances. Illustrative example is given. Input chattering is remarkably eliminated and trajectory tracking is effectively achieved. [ABSTRACT FROM AUTHOR]

This paper presents the advances of a research using a combination of recurrent and feed-forward neural networks for long term prediction of chaotic time series. It is known that point-to-point, long term prediction for chaotic time series is not possible; however, in this research we are looking for ways to build dynamical systems using artificial neural network, that contain the same characteristics as the unknown systems producing a time series. The created systems should be such that they have chaotic invariants similar to the ones presented in the time series. Being able to create such system, the bounds of the predictions may be defined. We present some general concepts related to chaos, dynamical systems and artificial neural networks and present one model that, if not able to predict yet, is able to autonomously oscillate in bounded limits and in a chaotic way. Some experimental results and future work is also presented. [ABSTRACT FROM AUTHOR]