A Simple Jerky Dynamics,Genesio System

The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we show that an algebraically simple system, the Genesio system can be recast into a jerky dynamics and its jerk equation can be derived from one-dimensional Newtonian equation. We also investigate the global dynamical properties of the corresponding jerk system.

Correlation between jerky flow and jerky dynamics in a nanoscratch on a metallic glass film

Chaos has been well understood in dynamic system, however, how the chaotic behavior occur in jerky flow in material, is still not clear, and is lack of specific chaotic attractor. Here the jerky evolution of lateral force and the stair-like fluctuation of lateral displacement are observed for Ni62 Nb38(at.%) metallic glass film during nanoscratch process. This jerky flow is investigated by using the largest Lyapunov exponent, Kolmogorov entropy and fractal dimension, and chaotic behavior of lateral force-time and normal displacement-lateral displacement sequences is verified. In addition to time series analysis, it is found that jerk equation can be used to describe the jerky flow of the metallic-glass film during nanoscratch. More importantly, unambiguous chaotic attractor is presented by jerky dynamics using "jerk"-singularities, namely the total change rate of lateral force relative to scratch time. These reveal an inner connection between jerky flow and jerky dynamics in nanoscratch of a metallic-glass film.

Newtonian Jerky Dynamics and Inertial Instability

Newtonian jerky dynamics is applied to inertial instability analysis to study the nonlinear features of atmospheric motion under the action of variable forces. Theoretical analysis of the Newtonian jerky function is used to clarify the criteria for inertial instability, including the influences of the meridional distributions of absolute vorticity （ζg） and planetary vorticity （the ζ effect）. The results indicate that the meridional structure of absolute vorticity plays a fundamental role in the dynamic features of inertial motion. Including only the ζ effect （with the assumptionof constant ζg） does not change the instability criteria or the dynamic features of the flow, but combining the β effect with meridional variations of ζg introduces nonlinearities that significantly influence the instability criteria. Numerical analysis is used to derive time series of position, velocity, and acceleration under different sets of parameters, as well as their trajectories in phase space. The time evolution of kinematic variables indicates that a regular wave-like change in acceleration corresponds to steady wave-like variations in position and velocity, while a rapid growth in acceleration （caused by a rapid intensification in the force acting on ,the parcel） corresponds to track shifts and abrupt changes in direction. Stable limiting cases under the f- and f-plane approximations yield periodic wave-like solutions, while unstable limiting cases yield exponential growth in all variables. Perturbing the value of absolute vorticity at the initial position （ζ0） results in significant changes in the stability and dynamic features of the motion. Enhancement of the nonlinear term may cause chaotic behavior to emerge, suggesting a limit to the predictability of inertial motion.