On the global attractivity and oscillations in a class of second-order difference equations from macroeconomics

El-Morshedy, Hassan A.

doi:10.1080/10236191003730548

Cited by 7 publications

(6 citation statements)

References 13 publications

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“…Also see [22]. In [4], El-Morshedy improves the convergence results of [10] for (2) and also gives necessary and sufficient conditions for the occurrence of oscillations. The boundedness of solutions of ( 2) is studied in [19] and periodic and monotone solutions of (2) are discussed in [23].…”

Section: Introductionmentioning

confidence: 82%

Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

Sedaghat

2013

Journal of Difference Equations and Applications

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Non-autonomous, higher order difference equations of type! with real variables and parameters have appeared frequently in the literature. These equations are well defined on Banach algebras, and existing convergence results can be generalized from real numbers to algebras. Through this generalization and by using a recently obtained semiconjugate factorization of the above equation, new sufficient conditions are obtained for the convergence to zero of all solutions of nonlinear difference equations of the above type. Where reduction of order is possible, these conditions extend the ranges of parameters for which the origin is a global attractor even in the case of real variables and parameters.

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Section: Introductionmentioning

confidence: 82%

Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

Sedaghat

2013

Journal of Difference Equations and Applications

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“…In [3], El-Morshedy improves the convergence results of [9] for (2) and also gives necessary and sufficient conditions for the occurrence of oscillations. The boundedness of solutions of ( 2) is studied in [16] and periodic and monotone solutions of (2) are discussed in [19].…”

Section: Introductionmentioning

confidence: 84%

“…where a 0 , a 1 , a 2 , b 1 , b 2 ∈ R and g : R → R. If a 2 = b 2 = 0 then (24) reduces to an autonomous version of the second-order equation (3). We assume here that b 2 = 0.…”

Section: Boundedness and Periodicitymentioning

confidence: 99%

Reduction of order, periodicity and boundedness in a class of nonlinear, higher order difference equations

Sedaghat

2013

Computers & Mathematics with Applications

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We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and economics. By extending some recent results to cases where characteristic polynomials of the linear expressions have complex roots, we obtain new results on boundedness and the existence of periodic solutions for equations of order 3 or greater.

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“…The condition (SH3) of Theorem 3.5.2 in [6] involves the first Lyapunov coefficient. In order to get it, we compute the normal form of system (5). Applying an invertible linear transformation (w 1 , w 2 ) T = H 2 (ϕ, ψ) T , we change the mapping in (5) into the mapping…”

Section: 1mentioning

confidence: 99%

“…In 2005, Sedaghat [15] presented both the sufficient conditions for the global attractivity of the fixed point and the conditions that the solutions produce the persistent oscillations, and then showed that the solutions exhibit strange and complex behaviors. In 2011, El-Morshedy [5] obtained the new global attractivity criteria by a Lyapunov-like method and the necessary and sufficient condition for the oscillation by comparison with a second-order linear difference equation with positive coefficients. If the function f is a polynomial with degree 3, Sushko, Puu and Gardini [16] investigated the Neimark-Sacker bifurcation.…”

mentioning

confidence: 99%

Two codimension-two bifurcations of a second-order difference equation from macroeconomics

Zhong¹,

Deng²

2018

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper we mainly investigate two codimension-two bifurcations of a second-order difference equation from macroeconomics. Applying the center manifold theorem and the normal form analysis, we firstly give the parameter conditions for the generalized flip bifurcation, and prove that the system does not produce a strong resonance. Then, we compute the normal forms to obtain the parameter conditions for the Neimark-Sacker bifurcation, from which we present the conditions for the Chenciner bifurcation. In order to verify the correctness of our results, we also numerically simulate a half stable invariant circle and two invariant circles, one stable and one unstable, arising from the Chenciner bifurcation.

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On the global attractivity and oscillations in a class of second-order difference equations from macroeconomics

Abstract: New global attractivity criteria are obtained for the second order difference equation

Cited by 7 publications

References 13 publications

Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

Reduction of order, periodicity and boundedness in a class of nonlinear, higher order difference equations

Two codimension-two bifurcations of a second-order difference equation from macroeconomics

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