A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos...

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, m...

In this paper, we derive new results for global chaos control of chaotic systems via sliding control. We also explore the analysis and global chaos control of the hyperchaotic Li system (2005) using sliding control. The global chaos control results via sliding control have been established using Lyapunov stability theory. Numerical simulations using MATLAB are shown to validate and depict the e...

A typical two-dimensional airfoil with freeplay nonlinearity in pitch undergoing subsonic flow is studied via numerical integrationmethods.Due to the existence of the discontinuous nonlinearity, the classical fourth-order Runge-Kutta (RK4) method cannot capture the aeroelastic response accurately. Particularly, it is because the RK4 method is incapable of detecting the discontinuous points of t...

The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here I review a variety of invariant measures for quantifying chaotic dynamics in relativity that exploit the coordinate independence of fractal dimensions and symbolic entropies. 1 Time and chaos Historically, chaos theory was developed for Newtonian dynamics where time and spac...

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