A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions andDirac–Delta functions as th...

We will prove the presence of chaotic motion in the Lorenz five-component atmospheric system model using the Melnikov function method developed by Holmes and Marsden for Hamiltonian systems on Lie Groups.  2002 Elsevier Science B.V. All rights reserved. PACS: 02.20.Sv; 02.30.Hg; 02.40.-k; 92.60.-e

The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator for a specific parametric choice (| α |= β) is studied. The existence of different attractors in the system parameters (f − ω) domain is examined and a detailed account of various steady states for fixed damping is presented. Transition from quasiperiodic to periodic motion through chaotic oscillations is reported. The i...

Analysis and controlling of bifurcation for a class of chaotic Van der PolDuffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is investigated. Based on the center manifold theory and normal form reduction, the stability index of bifurcation solution i...

In this paper, a method for identifying the chaotic state of duffing oscillator is proposed where the duffing oscillator is used for weak signal detection. This method is based on frequency spectrum analysis and filtering. Some relative aspects of this method for practical using are studied in details too. The proposed method has three properties; reasonable calculation complexity, robustness t...

this paper addresses a nonlinear observer based control scheme to synchronize chaotic systems subject to uncertainties and external disturbances. it is assumed that the dynamic of slave system is not completely known. in order to compensate for the system perturbation resulting from parameter variations and mismodeling phenomena, an adaptive neural network observer is employed to handle this pr...

An asymptotically stable direct adaptive fuzzy PI sliding mode controller is proposed for a class of nonlinear uncertain systems. In contrast to other existing approaches of handling disturbances, the proposed approach does not require this bound to be known, only requiring that it exists. Moreover, a PI control structure is used to attenuate chattering. The approach is applied to stabilize an ...

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) a...