The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of...

This study analyzes the chaotic behavior of a micromechanical resonator with electrostatic forces on both sides and investigates the control of chaos. A phase portrait, maximum Lyapunov exponent and bifurcation diagram are used to find the chaotic dynamics of this micro-electro-mechanical system (MEMS). To suppress chaotic motion, a robust fuzzy sliding mode controller (FSMC) is designed to tur...

An analysis of Parrondo’s games with different chaotic switching strategies is carried out. We generalize a fair way to compare between different switching strategies. The performance of Parrondo’s games with chaotic switching strategies is compared to random and periodic switching strategies. The rate of winning of Parrondo’s games with chaotic switching strategies depends on coefficient(s) de...

In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The complex dynamical behaviors of the system are further investigated by means of eigenvalue structures and various attractors. The chaotic system examined in MATLAB 2010. The Oscillator...

A long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. Considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. In this paper, we propose and analyze a three-axis optimal control on the s...

Accurate performance prediction is key to the design of high performance machines. It is shown here that connection clearance and component flexibility can result in machine dynamic behaviors that are hypersensitive to small variations of system design parameters and operating conditions. These hypersensitivities, which can limit the usefulness of computer dynamic simulations for design, are as...

It has been known that noise can enhance the temporal regularity of dynamical systems that exhibit a bursting behavior--the phenomenon of coherence resonance. But can the phenomenon be expected for nonbursting chaotic systems? We present a theoretical argument based on the idea of time-scale matching and provide experimental evidence with a chaotic electronic circuit for coherence resonance in ...

As an important application of chaotic dynamical systems, chaos-based secure communication and cryptography attracted continuous interest over the last decade. It studies methods of controlling deterministic systems with chaotic behavior. Moreover, it is easy to notice the possibility of substantial variation of the characteristics of chaotic systems by relatively small variations of their para...

We numerically investigate chaotic behavior in autonomous nonlinear models of fractional order. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in ð0; 1 , based on frequency domain arguments, and the resulting equivalent models are studied. Two chaotic models are considered in this study; an electronic chaotic oscillator, ...