Global eriodicity and complete integrability of discrete dynamical systems

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Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.

N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Variational principles for nonlinear dynamical systems

A variational method for Hamiltonian systems is analyzed. Two different variationalcharacterization for the frequency of nonlinear oscillations is also suppliedfor non-Hamiltonian systems

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Fusion of the extended modified liquid drop model for nucleation and dynamical nucleation theory

We present a new phenomenological approach to nucleation, based on the combination of the extended modified liquid drop model and dynamical nucleation theory. The new model proposes a new cluster definition, which properly includes the effect of fluctuations, and it is consistent both thermodynamically and kinetically. The model is able to predict successfully the free energy of formation of the critical nucleus, using only macroscopic thermodynamic properties. It also accounts for the spinodal and provides excellent agreement with the result of recent simulations.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

An ecological systems theory approach in looking at mental health care barriers in the latino community

Tesis (Doctorado en Filosofía con Orientación en Trabajo Social y Políticas Comparadas de Bienestar Social) U.A.N.L. Facultad de Filosofía Letras y Escuela de Graduados de la Universidad de Arlington, Texas, 2008

The Power and Promise of Developmental Systems Theory

I argue that it is time for many feminists to rethink their attitudes towards evolutionary biology, not because feminists have been wrong to be deeply sceptical about many of its claims, both explicit and implicit, but because biology itself has changed. A new appreciation for the importance of development in biology has become mainstream and a new ontology, associated with developmental systems theory (DST), has been introduced over the last two decades. This turn challenges some of the features of evolutionary biology that have most troubled feminists. DST undermines the idea of biologicales sence and challenges both nature /nurture and nature/culture distinctions. Freed from these conceptual constraints, evolutionary biology no longer poses the problems that have justified feminist scepticism. Indeed, feminists have already found useful applications for DST and I argue that they should expand their use of DST to support more radical and wide-ranging political theories.

Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based On P

I present a novel design methodology for the synthesis of automatic controllers, together with a computational environment---the Control Engineer's Workbench---integrating a suite of programs that automatically analyze and design controllers for high-performance, global control of nonlinear systems. This work demonstrates that difficult control synthesis tasks can be automated, using programs that actively exploit and efficiently represent knowledge of nonlinear dynamics and phase space and effectively use the representation to guide and perform the control design. The Control Engineer's Workbench combines powerful numerical and symbolic computations with artificial intelligence reasoning techniques. As a demonstration, the Workbench automatically designed a high-quality maglev controller that outperforms a previous linear design by a factor of 20.

A Dynamical Systems Model for Language Change

Formalizing linguists' intuitions of language change as a dynamical system, we quantify the time course of language change including sudden vs. gradual changes in languages. We apply the computer model to the historical loss of Verb Second from Old French to modern French, showing that otherwise adequate grammatical theories can fail our new evolutionary criterion.

Discrete Dynamical Systems

Exercises and solutions for a third or fourth year maths course. Diagrams for the questions are all together in the support.zip file, as .eps files