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- Title
GLOBAL DYNAMICS OF CERTAIN MIX MONOTONE DIFFERENCE EQUATION VIA CENTER MANIFOLD THEORY AND THEORY OF MONOTONE MAPS.
- Authors
KULENOVIĆ, MUSTAFA R. S.; NURKANOVIĆ, MEHMED; NURKANOVIĆ, ZEHRA
- Abstract
We investigate the global dynamics of the following rational difference equation of second order ... where the parameters A and E are positive real numbers and the initial conditions xx-1 and x0 are arbitrary non-negative real numbers such that xx-1 + x0 0. The transition function associated with the right-hand side of this equation is always increasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric values. The unique feature of this equation is that the second iterate of the map associated with this transition function changes from strongly competitive to strongly cooperative. Our main tool for studying the global dynamics of this equation is the theory of monotone maps while the local stability is determined by using center manifold theory in the case of the nonhyperbolic equilibrium point.
- Subjects
DIFFERENCE equations; REAL numbers; STATISTICAL equilibrium; ALGEBRAIC equations; NUMERICAL calculations
- Publication
Sarajevo Journal of Mathematics, 2019, Vol 15, Issue 2, p129
- ISSN
1840-0655
- Publication type
Article
- DOI
10.5644/SJM.15.02.01