168 research outputs found
Chaos
No full textIn this chapter, we first precise the concept of dynamical systems, and then we introduce the concept of chaos, which is characterized by a sensitive dependence on initial conditions. To quantify this, dynamical (Lyapunov exponents) and probabilistic (dimensions) measures are introduced
Embedding Dimension and Mutual Information
No full textIn this chapter, we introduce the concept of the embedding dimension, as the smallest topological dimension required to ensure that an object described by simpler (often scalar) time series can be embedded in a higher topological dimension
Bifurcations
No full textMany dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the orbits can change dramatically. In the present chapter, we first provide the definition of homoclinic and heteroclinic orbits and then a summary about local bifurcations for both the continuous case and the discrete-time case. Global bifurcations will be presented in the next following chapter
Preface (Editorial)
No full textThis book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry
Introduction
No full textIn this Introduction, we illustrate the genesis of the theory of chaos as by-product of the study of nonlinear systems in physics and meteorology. Then, we introduce the notion of nonlinearities in economics and the extension of the methods and the analyses devised in hard sciences not only for understanding the dynamics but, also, for predicting and controlling them. After that, we describe the organization of this book that, in the first three parts, has the objective of providing the needed knowledge to anyone who would like to study nonlinear phenomena in economics. The fourth part, instead, shows how the aforementioned methods and analyses can be applied to economics and gives an account of current research on the topic
Nonlinearities in Economics An Interdisciplinary Approach to Economic Dynamics, Growth and Cycles
No full textThis interdisciplinary book argues that the economy has an underlying non-linear structure and that business cycles are endogenous, which allows a greater explanatory power with respect to the traditional assumption that dynamics are stochastic and shocks are exogenous.
The first part of this work is formal-methodological and provides the mathematical background needed for the remainder, while the second part presents the view that signal processing involves construction and deconstruction of information and that the efficacy of this process can be measured. The third part focuses on economics and provides the related background and literature on economic dynamics and the fourth part is devoted to new perspectives in understanding nonlinearities in economic dynamics: growth and cycles.
By pursuing this approach, the book seeks to (1) determine whether, and if so where, common features exist, (2) discover some hidden features of economic dynamics, and (3) highlight specific indicators of structural changes in time series. Accordingly, it is a must read for everyone interested in a better understanding of economic dynamics, business cycles, econometrics and complex systems, as well as non-linear dynamics and chaos theory
Periodic orbit analysis demonstrates genetic constraints, variability, and switching in Drosophila courtship behavior
No full textRuedi Stoop and Benjamin I. Arthur, Jr.
Institute for Neuroinformatics ETHZ/UNIZH, Winterthurerstr.
We use symbolic dynamics to describe Drosophila courtship communication. We posit that behavior should be defined in terms of irreducible periodic orbits of fundamental acts. This leads to a first operational definition of behavior, which allows for a fine grained quantitative analysis of behavior. We obtain evidence that during Drosophila courtship, individual characteristics of the protagonists are exchanged (predominantly from the male to the female) and that males in the presence of fruitless males perform a behavioral switch from male to female behavio
Exploiting deterministic features in apparently stochastic data
No full textMany processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach’s results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime
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