Global dynamics of quadratic second order difference equation in the first quadrant
نویسندگان
چکیده
We investigate the global behavior of a quadratic second order difference equation xnþ1 1⁄4 Axn þ Bxnxn 1 þ Cx 2 n 1 þ Dxn þ Exn 1 þ F; n 1⁄4 0;1; . . . with non-negative parameters and initial conditions. We find the global behavior for all ranges of parameters and determine the basins of attraction of all equilibrium points. 2013 Elsevier Inc. All rights reserved.
منابع مشابه
Global dynamics of cubic second order difference equation in the first quadrant
We investigate the global behavior of a cubic second order difference equation xn+1 = Ax3 n + Bx 2 nxn–1 + Cxnx 2 n–1 + Dx 3 n–1 + Ex 2 n + Fxnxn–1 + Gx 2 n–1 + Hxn + Ixn–1 + J, n = 0, 1, . . . , with nonnegative parameters and initial conditions. We establish the relations for the local stability of equilibriums and the existence of period-two solutions. We then use this result to give global ...
متن کاملDynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$
The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...
متن کاملA nonlinear second order field equation – similarity solutions and relation to a Bellmann-type equation - Applications to Maxwellian Molecules
In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian...
متن کاملSolving A Fractional Program with Second Order Cone Constraint
We consider a fractional program with both linear and quadratic equation in numerator and denominator having second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a second order cone programming (SOCP) problem. For the quadratic fractional case, using a relaxation, the problem is reduced to a semi-definite optimization (SDO) program. The p...
متن کاملOn the Second Order Behaviour of the Bootstrap of L_1 Regression Estimators
We consider the second-order asymptotic properties of the bootstrap of L_1 regression estimators by looking at the difference between the L_1 estimator and its first-order approximation, where the latter is the minimizer of a quadratic approximation to the L_1 objective function. It is shown that the bootstrap distribution of the normed difference does not converge (eit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 227 شماره
صفحات -
تاریخ انتشار 2014