Chaotic time series data are observed routinely in experiments on physical systems and in
observations in the field. The authors review developments in the extraction of information of …

The problem of optimal control of the equilibrium states of the Lorenz system in both finite
and infinite time intervals has been studied. The optimal control functions ensuring …

" This study utilized coniJination of phase plots, time steps dstribution and adaptive time
steps Runge-Kutta and fifth order algorfthms to investigate a harmonically duffing osciliator …

This study utilised fractal disk dimension characterization to investigate the time evolution of
the Poincare sections of a harmonically excited Duffing oscillator. Multiple trajectories of the …

Statistical classical mechanics and quantum mechanics are developed and well-known
theories that represent a basis for modern physics. The two described theories are well …

To analyze a harmonically Van der Pol oscillator, this work used a combination of graphs,
time steps distribution, adaptive time steps Runge-Kutta, and fourth order algorithms. The …

" This study investigated the characterisation of the dynamic responses of 3-dimensional
Lorenz and Rӧsler models by Lyapunov's exponents using popular but laborious to …

The van der Pol equation is a nonlinear dynamical system found in a triode circuit. The
modified van der Pol equation is defined as d2x/dt2-u (1-x2) dx/dt+ x3= Bcos (t). This …

By drawing exact bifurcation diagrams, it is confirmed that the Melnikov curve of
homoclinicity gives a good prediction for the onset of the chaotic attractor bifurcated from the …

This paper adopted five popular Runge-Kutta algorithms ranging from order two to five as
well as modified order five to investigate the chaotic behavior of the excited Duffing …