Using the normalised wavefunction in momentum space, in the context of the statistical model, we have studied the properties of the coupling constant which exhibits the asymptotic freedom and confinement properties.
Theoretical investigation on the propagation of ion-acoustic waves in an unmagnetized self-gravitating plasma has been made for the existence of solitary waves using the reductive perturbation method. It is observed that nonlinear excitations follow a coupled third-order partial differential equation which is slightly different from the usual case of coupled Korteweg-de Vries (K-dV) system. It appears that the system so deduced is a two-component generalization of the previous one derived by Paul et al. (1999) in which it was shown that ion-acoustic solitary waves can not exist in such system.
Generalized synchronization between two different nonlinear systems under influence of noise is studied with the help of an electronic circuit and numerical experiment. In the present case, we have studied the phenomena of generalized synchronization between the Lorenz system and another nonlinear system (modified Lorenz) proposed in Ray et al. (2011, “On the Study of Chaotic Systems With Non-Horseshoe Template,” Frontier in the Study of Chaotic Dynamical Systems With Open Problems, Vol. 16, E. Zeraoulia and J. C. Sprott, eds., World Scientific, Singapore, pp. 85–103) from the perspective of electronic circuits and corresponding data collected digitally. Variations of the synchronization threshold with coupling (between driver and driven system) and noise intensity have been studied in detail. Later, experimental results are also proved numerically. It is shown that in certain cases, noise enhances generalized synchronization, and in another it destroys generalized synchronization. Numerical studies in the latter part have also proved results obtained experimentally.
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