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.

The present paper represents an analytical solution of fingering phonomenon arising in double phase flow through homogeneous media under certain initial & boundary condition using techniques of calculus of variation and similarity theory. The numerical and graphical representation of solution has been given the graph of saturatin F(η) of injected liquid, is increasing after η = 0.5 for t > 0, which indicates that when injected liquid entries into native liquid at common-interface, then suddenly the native liquid enters into injected liquid due to difference in wettability. Hence initial saturation will decrease and then after η > 0.5 the saturation uniformly increases parabolically which is physically consistent with the available theory.

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.