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...

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.

Quasi-periodic route to chaos is a common feature in DC-DC switching converters like the Boost and the Buck-Boost. A periodic orbit bifurcates into a T torus through a Neimark-Sacker bifurcation, and then, quasi-periodic behavior is obtained. Further changes in the parameters may breakdown such torus resulting in chaotic behavior. Analytical expressions are deduced for the stability character o...

In this paper, a periodic parametric perturbation was designed for controlling chaos and generating chaos (chaotification) from a three-dimensional autonomous system. When we added the small periodic parametric perturbations, the system became a non-autonomous system, which has abundant dynamics behavior. Periodic, chaotic and hyperchaos behaviors were identified by the Lyapunov exponents and b...

We show how periodic motions can be represented by a small number of eigenshapes that capture the whole dynamic mechanism of the motion. Spectral decomposition of a silhouette of a moving object serves as a basis for behavior classification by principle component analysis. The boundary contour of the walking dog, for example, is first computed efficiently and accurately. After normalization, th...

used by TCP and other transport protocols — causes the transmission rate of a long-lived flow to oscillate. This paper is about the tendency of multiplexed flows on a bottleneck link to oscillate causing " aggregate periodic behavior ". As a consequence, bottleneck links can become underutilized, wasting capacity. One simple way to prevent this is to use larger buffers in the bottleneck router....

Lava dome eruptions commonly display fairly regular alternations between periods of high activity and periods of low or no activity. The time scale for these alternations is typically months to several years. Here we develop a generic model of magma discharge through a conduit from an open-system magma chamber with continuous replenishment. The model takes account of the principal controls on f...

Modeling of bioreactor with cell recycle based on a pseudo-homogeneous floc model is proposed to predict complex dynamic behavior. The model is based on interactive kinetics between substrate and dissolved oxygen, and takes into account the external mass transfer resistance around the biological floc. The investigation of the static and dynamic bifurcation of the model shows that periodic as we...