[PDF] Top 20 Global Dynamics of a Competitive System of Rational Difference Equations in the Plane

... a global invariant curve through a fixed point hyperbolic or not of a competitive map that is differentiable in a neighborhood of the fixed point, when at least one of two nonzero eigenvalues of the Jacobian ... See full document

... y, system () is cooperative. Competitive and cooperative maps are defined ...Strongly competitive systems of difference equations or strongly competitive maps are those for which the ... See full document

... for competitive systems in the plane, when one of the eigenvalues of the linearized system at an equili- brium (hyperbolic or non-hyperbolic) is by absolute value smaller than 1 while the other has ... See full document

... the global behavior of solu- tions to all systems () whose maps are bounded and thus provide answers to many of the open problems in ...the global dynamics of the system la- beled (, ) in ... See full document

... Each system has only one equilibrium point which is stable under some restriction to ...the global behavior of a sys- tem based on the knowledge of its present ...possible global behaviors of the ... See full document

... the system has no prime period-two ...the global behavior of a system based on the knowledge of its present ...possible global behaviors of the system and deter- mining which initial ... See full document

... Although difference equations are sometimes very simple in their forms ,they are extremely difficult to understand thoroughly the behavior of their solutions ...studied global behavior of nonlinear ... See full document

... years, rational difference equations have attracted the attention of many researchers for varied ...nonlinear equations which are, in some cases, treatable but whose dynamics present some new ... See full document

... exponential rational difference ...of system () and ...of system () and () is locally as well as globally asymptotically stable under certain parametric ...the global behavior of a ... See full document

... Competitive and cooperative systems of the form () were studied by many authors such as Clark and Kulenović [], Clark, Kulenović and Selgrade [], Hirsch and Smith [], Ku- lenović and Ladas [], Kulenović and ... See full document

... the global stability of the boundary order- limit cycle have been obtained for the first time, which can be used to compare the efficiency of a single control tactic alone with the efficiency of more than one ... See full document

... Thus, the solution is bounded and persists and the proof is complete. □ Conclusion 1. In this paper , we study a asymptotic behavior of solutions of a general class of difference Equation (1.1). Our results extend ... See full document

... prove global existence of solutions to (1)-(3) (see, for example [19]), there are several methods such as the method of comparison with corresponding ordinary differential equations, method of invariant ... See full document

... a difference field F, the Lie algebra A of its evolutionary derivations (or evolutionary vector fields) which is a subalgebra of Der F and discuss algebraic properties of the noncommutative ring of ... See full document

... some global dynamic scenarios for competitive maps which are motivated by some dynamic scenarios for Equation ...different global dynamic scenarios for Equation (1) will be examples of general ... See full document

... 5. The methodic of forming a rational structure of a distributed production base of transport divisions in the pipeline industry was created. Unlike existing, this methodic takes into account technological factors ... See full document

... Putnam-type equations,” Nonlinear Analysis: Theory, Methods & Applications, ...“The global attractivity of a higher order rational difference ... See full document

... The nature of many biological systems naturally leads to their study by means of a discrete variable. Particular examples include population dynamics and genetics. Some elementary models of biological phenomena, ... See full document

... This paper presents the use of a variational iteration method for systems of nonlinear difference equations. This technique is a powerful tool for solving various difference equations and can also be applied ... See full document

... difference equations, although their forms (or expressions) look very simple, it is extremely difficult to understand thoroughly the global behaviors of their ... See full document