Multiple attractors and business fluctuations in a nonlinear macro-model with equity rationing

• Published in: Mathematical and computer modelling Vol. 53; no. 5-6; pp. 1298 - 1309
• Main Authors: Dieci, Roberto, Gallegati, Mauro
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2011; Elsevier
• Subjects: Bifurcation analysis; business enterprises; Business fluctuations; debt; Exact sciences and technology; Global analysis, analysis on manifolds; income; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Multiple attractors; Nonlinear dynamics; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; time series analysis; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Nonlinear dynamics; Business fluctuations; Multiple attractors; Bifurcation analysis; Time series; Bifurcation; Discrete system; Dynamical system; Attractor; Applied mathematics; Non linear model; Discrete time; Two-dimensional calculations; Mathematical model; Computer aided analysis
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2010.12.016

A stylized model of business fluctuations is developed, where investment and debt accumulation are responsible for the endogenous dynamics of income. Despite the simplicity of the model, the resulting nonlinear, two-dimensional discrete-time dynamical system displays a wide range of possible dynamic outcomes. If a key parameter, representing the propensity to invest, shifts exogenously from low to high values, a transition across qualitatively different long-run scenarios is observed, associated to different levels of economic activity. Moreover, coexistence of attractors and path-dependence characterize the dynamics for an intermediate range of such a parameter. The impact of exogenous disturbances on such situations results in aperiodic time series subject to unpredictable booms and slumps.