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Nonlinear properties of ion-acoustic waves (IAWs) are studied in electron-ion (EI) degenerate plasma with the electron exchange-correlation effects by using the quantum hydrodynamic (QHD) model. To investigate arbitrary amplitude IAWs, we have reduced the model equations into a system of ordinary differential equations using a traveling wave transformation. Computational investigations have been performed to examine the combined effect of Bohm potential and exchange-correlation potential significantly modifies the dynamics of IAWs by employing the concept of dynamical systems. The equilibrium points of the model are determined and its stability natures are analyzed. The phase portrait and Poincaré return map of the dynamical system are displayed numerically. Quasiperiodic as well as chaotic dynamics of the system are confirmed through the Poincaré return map diagrams.

In this paper, we have investigated the decay process of the kinetic energy density spectrum in a homogeneous isotropic turbulence. It has been shown that the spectral equation for the energy density spectrum E(k) with modified form of energy transfer spectrum due to Obukhov (Compt. Rend. Acad. Sci. U. R. S. S 32:22–24, 1941) and as restricted to early-period decay process, admits of a class of self-preserving solution. Such solutions are identified by their asymptotic behaviour e.g, $$E(k) \sim k^{\frac{2-3c}{c}} ( k \rightarrow 0)$$ E(k)∼k2-3cc(k→0) where $$c( < \frac{2}{3})$$ c(<23) is a parameter and $$E(k) \sim k^{-\frac{5}{3}} ( k \rightarrow \infty )$$ E(k)∼k-53(k→∞) . Numerical computations of some selective spectra, corresponding to values of c e.g., $$c=\frac{1}{2}, \frac{2}{5}, \frac{1}{3}$$ c=12,25,13 and $$\frac{2}{7}$$ 27 are then accomplished over the entire range of wave numbers concerned (excluding the viscous dissipation range). We attempt to find a class of non viscous self-preserving solution using the modified Obukhov form (cf Hinze An introduction to its mechanism and theory, 1975) for the spectrum function F(k, t) and compute them numerically. Finally, stability analysis is carried out for the above mentioned self-preserving spectra and it is shown that they represent different degrees of unstable situations.

AbstractIn this communication, emphasis is given to consider different types of growth from phenomenological point of view in a generalized manner. Truly linear behaviour of the system is examined with the help of phenomenological approach. It is also shown that the parameters of a biological growth following West-type or von Bertalanffy equations are controlled by two phenomenological coefficients, instead of one as found in the literature. They contribute in a different manner in energy intake and metabolic cost. As a result, two different growth mechanisms controlling resultant growth process behave differently in case of energy intake and metabolic cost. It is also established that some phenomenological classes that may indicate a common growth mechanism with different degree of intensity, are following generalized features. As a consequence, they can be grouped with a generalized solution and differential equation. A phenomenological class representing non-linear growth process is also proposed here from theoretical consideration. Some well-known classes are also reexamined with some of their minute properties. Special attention is given to find the role of phenomenological coefficients in determining the growth feature of a phenomenological class and it is found that phenomenological coefficients of a class may lead to a specific type of growth that is generally presented by different phenomenological class.

In this paper, dynamical behavior of simple prey-predator model with Holling type II functional response involving additional food for predator along with intraspecific competition of prey is proposed and analyzed. The stability criteria of solutions are investigated by varying quantity and quality of additional food and intraspecific competition of prey population. Conditions for Hopf bifurcation are derived analytically. Numerical simulation results are presented to observe the time evolution of the system. This study may be useful to understand the effects of intraspecific competition in real world ecological systems.

In this paper, we propose a susceptible-exposed-infected prey–predator model supplying additional food to predator. We discuss the existence and the local stability conditions of both the disease free and endemic equilibrium points. Basic reproduction number is determined. The impact of additional food on infected prey population is discussed. Numerical simulation results establish that there exists a critical infection rate above which disease present in the system in absence of additional food. However, in such case supply of suitable additional food can make the system disease free. We compute the disease free regions in various parametric planes. Effects of variation of latent period is presented. Season dependent infection rate is also introduce in the system and the role of additional food is discussed. The main goal of this study is to show the non-trivial consequences of providing additional food for controlling infection in a diseased predator–prey system. This study is aimed to introduce a new non-chemical method for controlling disease of prey population.

AbstractThis paper investigates the synchronization of Nuclear spin generator system. Sufficient theorem for the synchronization of Nuclear spin generator system are deduced. A scheme of secure communication based on the synchronization of Nuclear spin generator system is presented. Numerical simulation shows its feasibility.

AbstractIn this paper, we use nonlinear control method for synchronization of two identical chaotic generalized Lotka-Volterra system. The determination of the controller is based on the Lyapunov stability theory. Numerical simulation results are shown for demonstration.

AbstractGeneralized synchronization of two unidirectionally coupled dynamical systems is a generalization of identical synchronization. In this paper, we study a special case of generalized synchronization e.g., linear generalized synchronization of two Lü dynamical systems.