program

Wednesday, September 11 (CET time)

Abstracts of the contributions

Fabio Tramontana Università di Urbino, Italy

Bifurcations in nonlinear smooth maps: Theory

Nonlinear smooth maps in discrete time naturally arise in economic modelling and other fields where the values of the variable cannot change continuously and the state of the system changes at discrete steps. The variables’ motion is driven by systems of difference equations where the next step value of each variable is obtained by using the previous steps values of the same and/or the other variables. In particular, nonlinear smooth maps permit to obtain periodic motion and even chaotic motion already in one dimension. We will investigate the main local bifurcations and the main sources of complex dynamics.

Anastasiia Panchuk Institute of Mathematics National Academy of Sciences of Ukraine

Bifurcations in nonlinear smooth maps: Numerical methods

When dealing with nonlinear dynamical systems, one rarely can obtain explicit analytic results, since most related techniques are limited to rather simple functions. Often it is necessary to draw on computer simulations, using various numerical methods, in order to study possible bifurcations of invariant sets, especially those that include saddle or repelling fixed points or cycles, or even invariant sets of more complicated structure. This lecture presents several useful numerical techniques, which allow one to obtain major idea about asymptotic dynamics of a nonlinear map, in particular, about arising bifurcation phenomena and transformations of attractors.

Frank Westerhoff University of Bamberg, Germany

Nonlinear Economic Dynamics: A Primer

Numerous economic systems exhibit pronounced fluctuations over time, evident in the oscillation between bullish and bearish trends in financial markets, the cyclical fluctuations within the real economy, and the emergence of bubbles and crashes in commodity markets. Fortunately, dynamic nonlinear economic models offer a pathway to discerning the inherent drivers behind these market turbulences. In this lecture, we illuminate a spectrum of established models within this framework, underscoring their capacity to provide nuanced insights into market dynamics. Furthermore, we delve into the prospective applications of these models as policy instruments aimed at fortifying the stability of economic systems, thereby mitigating the impact of market volatility and fostering resilience in times of economic crises.

Domenico Massaro Department of Economics, Management and Quantitative Methods (DEMM), University of Milan, Italy

Macroeconomic Models with Heterogeneous Expectations: Empirical Evidence and Policy Implications

The lecture discusses behavioral macroeconomic models characterized by boundedly rational heterogeneous agents, who lack a full understanding of their complex environment and instead rely on simple decision heuristics. In the first part of the lecture, we present empirical evidence for heuristic switching behavior using both aggregate time series and survey data. The second part focuses on laboratory experiments, exploring the conditions under which a complex macro-system of interacting agents may or may not converge on the rational equilibrium outcome. Furthermore, we will examine the policy implications of this coordination failure and discuss how policies can assist in managing the self-organization process of heterogeneous expectations.