Dynamics of a second‑order nonlinear diference system with exponents

Document Type : Original Article

Authors

1 Department of Mathematics, St. John’s College, Anchal, Kerala, India.

2 Department of Mathematics, Mar Ivanios College, Research Centre, University of Kerala, Thiruvananthapuram, India.

Abstract

In this paper, we study the persistence, boundedness, convergence, invariance and
global asymptotic behavior of the positive solutions of the second-order diference
system
xn+1 = α1 + ae−xn−1 + byne−yn−1 ,
yn+1 = α2 + ce−yn−1 + dxne−xn−1 n = 0, 1, 2, ... where α1, α2, a, b, c, d are
positive real numbers and the initial conditions x−1, x0, y−1, y0 are arbitrary nonnegative
numbers.

Keywords