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This article is concerned with the following rational difference equation xn+1 = (βxn-3)/A+Bxn-1xn-3 with the initial conditions, x-3 = d, x-2 = c, x-1 = b, and x0 = a are arbitrary real numbers, β, A and B are arbitrary constants. A detailed analytical study of the convergence of the solutions including their dependence on parameters and initial conditions is investigated. The local stability and global attractivity of the difference equation's equilibrium points are discussed. The existence of periodic solutions in the proposed difference equation is also verified analytically. Moreover, numerical simulations are carried out to verify the correctness of the analytical results. [ABSTRACT FROM AUTHOR]

This article is concerned with the following rational difference equation xn+1 = βxn-3/A+Bxn-1xn-3 with the initial conditions, x-3 = d, x-2 = c, x-1 = b, and x0 = a are arbitrary real numbers, β, A and B are arbitrary constants. A detailed analytical study of the convergence of the solutions including their dependence on parameters and initial conditions is investigated. The local stability and global attractivity of the difference equation's equilibrium points are discussed. The existence of periodic solutions in the proposed difference equation is also verified analytically. Moreover, numerical simulations are carried out to verify the correctness of the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the convergence of “Leray-type” solutions of a magneto-hydro-dynamic system as the Rossby number approaches zero. The proofs are based on weak compactness arguments, interpolation estimates, and linear algebra methods. [ABSTRACT FROM PUBLISHER]