Economic Evolution and Structural Adjustment: Proceedings, Berkeley, California, USA, 1985

Since the beginning of the fifties, the ruling paradigm in the discipline of economics has been that of a competitive general equilibrium. Associated dynamic analyses have therefore been preoccupied with the stability of this equilibrium state, corresponding simply to studies of comparative statics. The need to permeate the boundaries of this paradigm in order to open up new pathways for genuine dynamic analysis is now pressing. The contributions contained in this volume spring from this very ambition. A growing circle of economists have recently been inspired by two distinct but complementary sources: (i) the pathbreaking work of Joseph Schumpeter, and (ii) recent contributions to physics, chemistry and theoretical biology. It turns out that problems which are firmly rooted in the economic discipline, such as innovation, technological change, business cycles and economic development, contain many clear parallels with phenomena from the natural sciences such as the slaving principle, adiabatic elimination and self- organization. In such dynamic worlds, adjustment processes and adaptive behaviour are modelled with the aid of the mathematical theory of nonlinear dynamical systems. The dynamics is defined for a much wider set of conditions or states than simply a set of competitive equilibria. A common objective is to study and classify ways in which the qualitative properties of each system change as the parameters describing the system vary

The Long-Wave Debate; Selected Papers from an IIASA International Meeting, Weimar, GDR, June 10-14, 1985

For over a century, some economists have pointed out that upswings and down turns in economic activity (along with some key economic variables) seem to follow a surprisingly regular pattern -- a pattern sometimes labeled simply "Kondratieff long waves" in honor of the Russian economist who first rigorously described some of the phenomena leading to these changes. What might to be causes and consequences of these long-term fluctuations? What is the relationship between these so-called long waves and other structural changes, technical revolutions, financial and monetary variables? Finally, if the mechanisms of long waves can be understood, will it be possible to avoid the recurrent recessions in economic development that are as painful for the less developed countries as for the developed ones -- be they socialist or capitalist in orientation? By invitation, an international panel of distinguished scholars met in Weimar, GDR, to discuss these fascinating questions about the existence and nature of long waves. This conference was organized and sponsored jointly by the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria and the Institute of Theory, History and Organization of Science of the GDR Academy of Sciences, Berlin. A select group of 30 contributions comprise THE LONG-WAVE DEBATE, which thus represents the state of the art in the theory and empirical observation of long-term economic cycles

Mathematical modeling of endocrine regulation subject to circadian rhythm

The 2017 Nobel Prize in Physiology or Medicine awarded for discoveries of molecular mechanisms controlling the circadian rhythm has called attention to the challenging area of nonlinear dynamics that deals with synchronization and entrainment of oscillations. Biological circadian clocks keep time in living organisms, orchestrating hormonal cycles and other periodic rhythms. The periodic oscillations of circadian pacemakers are self-sustained; at the same time, they are entrainable by external periodic signals that adjust characteristics of autonomous oscillations. Whereas modeling of biological oscillators is a well-established research topic, mathematical analysis of entrainment, i.e. the nonlinear phenomena imposed by periodic exogenous signals, remains an open problem. Along with sustained periodic rhythms, periodically forced oscillators can exhibit various “irregular” behaviors, such as quasiperiodic or chaotic trajectories. This paper presents an overview of the mathematical models of circadian rhythm with respect to endocrine regulation, as well as biological background. Dynamics of the human endocrine system, comprising numerous glands and hormones operating under neural control, are highly complex. Therefore, only endocrine subsystems (or axes) supporting certain biological functions are usually studied. Low-order dynamical models that capture the essential characteristics and interactions between a few hormones can than be derived. Goodwin's oscillator often serves as such a model and is widely regarded as a prototypical biological oscillator. A comparative analysis of forced dynamics arising in two versions of Goodwin's oscillator is provided in the present paper: the classical continuous oscillator and a more recent impulsive one, capturing e.g. pulsatile secretion of hormones due to neural regulation. The main finding of this study is that, while the continuous oscillator is always forced to a periodic solution by a sufficiently large exogenous signal amplitude, the impulsive one commonly exhibits a quasiperiodic or chaotic behavior due to non-smooth dynamics in entrainment.Team Tamas Keviczk