In this paper, a numerical study of natural convection in a trapezoidal cavity with left heated wall, right cold wall and filled with Cu – Al2 O3 and water hybrid nanofluid. The remaining walls of the cavity are kept at adiabatic. An enhancement in heat transfer is observed with the increase of three different parameters. Based upon the numerical predictions, the effect of Rayleigh number, inclination of the slopping wall, solid volume fraction of nanoparticles on flow and patterns as well tested. We found that acute slopping wall, high Rayleigh number and Cu – Al2 O3 nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle, effective thermal conductivity and viscosity as well as Rayleigh number.

A food chain model in which the top predator growing logistically has been proposed and studied. Two types of Holling’s functional responses type IV and type II have been used in the first trophic level and second trophic level respectively, in addition to Leslie-Gower in the third level. The properties of the solution are discussed. Since the boundary dynamics are affecting the dynamical behavior of the whole dynamical system, the linearization technique is used to study the stability of the subsystem of the proposed model. The persistence conditions of the obtained subsystem of the food chain are established. Finally, the model is simulated numerically to understand the global dynamics of the food chain under study.

In this research, some of Pareto properties from the first class are studied beside some of its theories and Pareto distribution parameters were obtained using a median amount. The amount of shape parameter contains a very complex model and its properties are difficult to know. In this paper, we approximated the mean and the variance using Tyler series of second degree derivation to obtain a mathematical model.

The paper introduces the concepts of (pi) over bar -strongly (resp., (pi) over bar -closure, (pi) over bar -weakly) form of continuous functions on bitopological spaces, furthermore, we introduce theorems, characterizing on the class of functions, show how it can be studied from a different point of view.

In this paper, Pareto distribution was studied using a standard Bayes estimator. A Pareto distribution of two parameters is investigated to find the approximation of (M.S.E) of the shape parameter by depending on Tyler series of two variables to propose a model mathematically.

In this paper, chaotic and periodic dynamics in a hybrid food chain system with Holling type IV and Lotka-Volterra responses are discussed. The system is observed to be dissipative. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov direct method. Chaos phenomena is characterized by attractors and bifurcation diagram. The effect of the controlling parameter of the model is investigated theoretically and numerically.

In this paper a technique of controlling chaotic behavior of a three species food chain model with Sokol-Howell functional response by involving intraspecific competition is discussed. The model is proved to be dissipative in the positive octant. Controlling conditions of chaotic behavior of the system are carried out. Stability analysis of the equilibrium points is analyzed. Lyaponuv exponents and bifurcation diagrams are used to study the complex dynamics of the model. The impact of the intraspecific competition in the dynamics of the foodchain model with Sokol-Howell response is investigated theoretically as well as numerically.

In this paper a technique of controlling chaotic behavior of a three species food chain model with Sokol-Howell functional response by involving intraspecific competition is discussed.The model is proved to be dissipative in the positive octant.Controlling conditions of chaotic behavior of the system are carried out.Stability analysis of the equilibrium points is analyzed.Lyaponuv exponents and bifurcation diagrams are used to study the complex dynamics of the model.The impact of the intraspecific competition in the dynamics of the food chain model with Sokol-Howell response is investigated theoretically as well as numerically.

In this paper a three-species of predator-prey food chain model with Holling type IV functional response is proposed.The boundedness of the solution of the model is discussed.Stability analysis of the system is carried out.The dynamics of the predator-prey food chain model with simplified Holling type IV functional response is investigated theoretically as well as numerically.

In this chapter, a three-species model of Leslie–Gower predator–prey food chain model with Sokol–Howell functional response is proposed. The boundedness of the solution of the model is discussed. Local and global stability analyses of the system are carried out. The dynamics of the predator–prey food chain model with Sokol–Howell functional response is investigated theoretically as well as numerically.

In this paper a three-species of Leslie-Gower predatorprey food chain model with Holling type IV functional response is proposed. The dissipativeness of the solution of the model is discussed. Local and global stability analyses of the system are carried out. The dynamics of the predator-prey food chain model with simplified Holling type IV functional response is investigated theoretically and numerically.