Hopf bifurcation in a dynamic IS–LM model with time delay

Abstract

Abstract. In this paper we investigate the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. With respect to the delay we show when the system is stable. Some numerical examples are finally given for justifying the theoretical results.

Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

“…Here, we use the term "Hopf" just to highlight the fact that a fixed point looses stability as the eigenvalues of the Jacobian at the fixed point cross the imaginary axis of the complex plain). De Cesare and Sportelli [13], Neamtu et al [14], Zhou and Li [15], and Sportelli et al [16] provide an interesting study on how limit cycles generated by Hopf bifurcations may arise in inflation models when there exists a finite lag between the accrual and payment of taxes, which implies a qualitative study of delay differential equations.…”

Uncertain and Stochastic Financial Models With Multiple Delays

“…At the same time, we have established the mean and mean square values. The presented analysis can be employed for other economic models or other processes as in [Mircea et al, 2009;Neamţu et al, 2007;You, 2008;Yao & Cui, 2010].…”

Homoclinic Bifurcation and Endogenous Cycles in the Dynamic IS-LM Model

“…In the next section, we use specific functional forms, joint with some numerical examples, to characterize the regions of the parametric space where the model exhibits a global indeterminate solution, and a lowgrowth trapping region, for an economically plausible range. In details, we assume I = Y R as in Neamtu et al (2007), we set L = kY hR as in Makovinyiova (2011), while we maintain a general savings function.…”

“…To overcome this problem, analyses of phase transitions from a determinate equilibrium to stable oscillations, and potentially chaotic motion, are explained either by imposing time-delayed feedbacks in the tax collection function (Cai 2005;De Cesare and Sportelli 2005;Fanti and Manfredi, 2007;Neamtu et al 2007;Tu et al 2013), or by looking at some specific parameter regions through the standard Hopf bifurcation theorem (Gandolfo 1997;Makovinyiova 2011;Guirao et al 2012;Neri and Venturi 2007). However, most of this literature confines herself entirely on the grounds of a local analysis (Slobodyan 2007;Chamley 1993;Farmer 1994, 1996;Benhabib et al , 2000, and so lacks providing a complete picture of the dynamics emerging outside the small neighborhood of the steady state, to whom we refer to as global indeterminacy.…”