‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an...

background: photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of spect images and results to errors in accuracy of quantitative measurements. this can be corrected via different physical or mathematical approaches. as the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘piece wise line...

A survey of the field related to control of chaotic systems is presented. Several major branches of research that are discussed are feed-forward ('non-feedback') control (based on periodic excitation of the system), the 'Ott-Grebogi-Yorke method' (based on the linearization of the Poincaré map), the 'Pyragas method' (based on a time-delayed feedback), traditional for control-engineering methods...

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase po...

Some chaotic properties of a classical particle interacting with a time-modulated barrier are studied. The dynamics of this problem is obtained by use of a two-dimensional nonlinear area-preserving map. The chaotic low energy region is characterized in terms of Lyapunov exponents. The time that the particle stays trapped in the well is such that the distributions of successive reflections, and ...

To solve the problems that whale optimization algorithm is easy to fall into local and slow convergence speed, improved proposed. Firstly, uses Skew Tent chaotic map initialize population, improve diversity of original population make individual position distribution whales more uniform; Secondly, nonlinear factor based on inverse incomplete ? function used balance global exploration developmen...

The presence of part-through cracks with limited length is one of the prevalent defects in the plate structures. Due to the slight effect of this type of damages on the frequency response of the plates, conventional vibration-based damage assessment could be a challenging task. In this study for the first time, a recently developed state-space method which is based on the chaotic excitation is ...