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Oscillation and stability in a delay model of a perennial grass. (English) Zbl 0856.39012
The authors study the oscillation and stability of the delay model of a perennial grass, x n+1 =ax n +(b+cx n-1 )e -x n , n=0,1,, where a,c(0,1) and b(0,), and where x -1 and x 0 are arbitrary positive initial conditions. It is shown that every solution is bounded and persists, every nonoscillatory or positive solution converges to a positive equilibrium, and for certain values of a and b there exists an attractive n cycle, for n a positive integer which increases as b increases.
MSC:
39A12Discrete version of topics in analysis
92B99Mathematical biology
39A11Stability of difference equations (MSC2000)