On the dynamics of positive solutions for the difference equation in a new population model

Abstract

In this paper we study the boundedness and the asymptotic behavior of positive solutions for the difference equationwhere a, b are positive constants, and the initial values x −1 , x 0 are nonnegative numbers.

Analytical Study of a System of Dierence Equation

“…However, there have not been any effective general methods to deal with the global behavior of rational difference equations of order greater than one so far. Therefore, the study of rational difference equations of order greater than one is worth further consideration see [1,2,3,4,5,6].…”

“…This can be attributed to the fact that many real life phenomena are modeled using difference equations. Some economical and biological examples can be seen in [1,7,8,9,10,11,12,13,14,15,16,17,2,3,4,5,6]. It is commonly known that nonlinear difference equations are able to produce and present sophisticated behaviors regardless their orders.…”

Global Dynamics of Some 3 × 6 Systems of Exponential Difference Equations

“…The beginning of 21 st century has witnessed an increasing interest in the population dynamics. Consequently, many works have been appeared on difference equations or systems of difference equations involving exponential terms (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and reference cited therein). For instance, Metwally et al [1] have investigated the dynamics of the following second-order difference equation:…”

“…After that Papaschinopoulos et al [5,6] have studied the asymptotic behavior of the positive solution of two-species model which 2 Discrete Dynamics in Nature and Society is also natural extension of single-species model represented in (3). In 2016, Wang and Feng [7] have investigated the dynamics of positive solution for the following difference equation which is naturally a new form of single-species model depicted in (1):…”

“…where , , , = 4, 5, ⋅ ⋅ ⋅ , 18 and the initial conditions 0 , −1 , 0 , −1 , 0 , −1 are arbitrary nonnegative real numbers. Equations (7) to (11) may be viewed as discrete-time population models in Mathematical Biology and biological parameters , , , = 4, 5, ⋅ ⋅ ⋅ , 18 can be interpretations as shown in Table 1.…”