Dynamics of Continuous, Discrete and Impulsive Systems, Series A Mathematical Analysis 2006, 13: 499–507. Irićanin B, Stević S: Some systems of nonlinear difference equations of higher order with periodic solutions. Automatically selecting between hundreds of powerful and in many cases original algorithms, the Wolfram Language provides both numerical and symbolic. Advances in Difference Equations 2007, 2007:-13. Papaschinopoulos G, Schinas CJ, Stefanidou G: On a -order system of lyness-type difference equations. Differential Equations and Dynamical Systems 1999, 7(2):181–196. Suggested Reading Section 3.5, Systems Described by Differential and Difference Equations, pages 101-111 Section 3. Papaschinopoulos G, Schinas CJ: Invariants for systems of two nonlinear difference equations. stant-coefficient differential equations for continuous-time systems. Communications on Applied Nonlinear Analysis 1998, 5(2):47–59. Papaschinopoulos G, Schinas CJ: On the behavior of the solutions of a system of two nonlinear difference equations. The techniques for solving differential equations based on numerical. It is in these complex systems where computer simulations and numerical methods are useful. Özban AY: On the system of rational difference equations, Applied Mathematics and Computation 2007, 188(1):833–837. Often, systems described by differential equations are so complex, or the systems that they describe are so large, that a purely analytical solution to the equations is not tractable. Özban AY: On the positive solutions of the system of rational difference equations, Journal of Mathematical Analysis and Applications 2006, 323(1):26–32. Communications on Applied Nonlinear Analysis 2001, 8(1):1–25. Grove EA, Ladas G, McGrath LC, Teixeira CT: Existence and behavior of solutions of a rational system. Venktesh, Department of Electrical Engineering, IIT Kanpur For more details on NPTEL visit. Çinar C, Yalçinkaya İ: On the positive solutions of difference equation system, , International Mathematical Journal 2004, 5(5):521–524.Ĭlark D, Kulenović MRS: A coupled system of rational difference equations. Lecture Series on Signals and System by Prof. Let us study now the problem of a nonlinear difference equation and how this can be implemented in Excel. The solution of first- and second-order linear differential. In order to prove main results of the paper we need an auxiliary result which is contained in the following simple lemma from number theory. They are often linear differential equations for which a sum of solutions remains a solution. Çinar C: On the positive solutions of the difference equation system, Applied Mathematics and Computation 2004, 158(2):303–305. Nonlinear first-order difference equations. Motivated by (1.8), we investigate the periodic character of the following two systems of difference equations: (1.9) (1.10) which can be considered as a natural generalizations of (1.8). 10.1006/jmaa.1997.5829Ĭamouzis E, Papaschinopoulos G: Global asymptotic behavior of positive solutions on the system of rational difference equations. An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. Journal of Mathematical Analysis and Applications 1998, 219(2):415–426. The Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain.Papaschinopoulos G, Schinas CJ: On a system of two nonlinear difference equations.
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