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absorbing set Advances in Discrete Appl assume assumptions asymptotic stability behavior bifurcation binary bounded chaotic companion matrix conjoined basis consider constant consumption converges defined delay difference equation denote difference equations differential equations Discrete Dynamical Systems discrete-time dynamic equations E-mail address Econom eigenvalues Elaydi equilibrium paths equivalent example exists exponential dichotomy faa(x finite Friedman rule function given global hantavirus Hence implies indeterminacy inequality infected initial interval invariant Kt+i Lemma linear Math Mathematics Subject Classification matrix method money holdings multiplicity Nishimura nonautonomous nonlinear nonnegative obtain October 12 optimal ordinary differential equations oscillation oscillatory paper parameter periodic solutions population positive integer Proposition quadratic random variables real number relative equilibria rodents roots satisfies sequence stochastic symplectic Theory tion topological topological entropy topologically conjugate unique vector Volterra Volterra difference equations xn+i zero solution