The notion of non-linear dynamics has become an energetic and fashionable field of work that is having a thoughtful effect on a wide variety of topics in present day technology. One such evolution of non-linear dynamics is the chaos theory. It is not about disorder, rather is about very complicated systems of order. However, the point of interest lies in bridging the gap between random nature o...

In this work it is shown that the Shannon entropy an efficient dynamical indicator provides a direct measure of diffusion rate and thus time-scale for instabilities arising when dealing with chaos. Its computation just involves solution Hamiltonian flow, variational equations are not required. After review theory behind approach, two particular applications presented; 4D symplectic map exoplane...

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

I propose that stiffness may be defined and quantified for nonlinear systems using Lyapunov exponents, and demonstrate the relationship that exists between stiffness and the fractal dimension of a strange attractor: that stiff chaos is thin chaos. What constitutes a stiff dynamical system? Stiffness is closely related to numerical methods [1]: the signature of stiffness in a problem is that, up...

In this work, an intelligent traffic light controller that incorporates very important personnel (VIP) movement is presented. VIP movement often cause chaos or in the worst case accident at cross junctions. Traffic quantity, waiting time and siren intensity are the inputs to the system. The fuzzy logic tool box in Matlab 7.0 was used to simulate the system. The results obtained from running the...

We present the first report on chaos synchronization between two unidirectionally linearly and non-linearly coupled systems with multiple time-delays and using the Razumikhin-Lyapunov approach find the existence and stability conditions for different synchronization regimes. The approach is tested on the famous nonlinear models-Ikeda, Mackey-Glass and Lang-Kobayashi systems.There is continued g...

Accurate and efficient modeling of the dynamics binary black holes (BBHs) is crucial to their detection parameter estimation through gravitational waves, both with LIGO/Virgo LISA. General BBH configurations will have misaligned spins eccentric orbits, eccentricity being particularly relevant at early times. Modeling these systems analytically numerically challenging. Even though 1.5 post-Newto...