It is a common assertion that, in a world with perfect markets and rational expectations, endogenous cycles could only arise under very unrealistic assumptions. This paper offers a short discussion on this claim and a review of the relevant contributions to the literature on deterministic fluctuations in competitive models. It is argued that these types of fluctuations are more easily obtained ...

In the spirit of Morse-Smale systems, the paper analyzes the structure of stability boundary of a stable equilibrium point for nonlinear dynamics subject to state limits. Presence of state limits implies that the underlying dynamics does not satisfy the Lipschitz condition for solution existence/uniqueness. There does not exist a smooth flow for the dynamics thus complicating traditional analys...

3 1.0 Introduction 4 1.1 Research Questions 5 1.2 Paper Structure 5 1.3 Methodology and Theoretical Framework 6 1.4Definitions 8 2.0 Limits to Predictive Understanding 11 2.1 Concept #1 Sensitive Dependance on Initial Conditions 11 2.2 Concept #2 Nonlinear Dynamics 14 2.3 Concept #3 Aggregate Complexity 18 3.0 Summary of Concepts 22 4.0 Discussion 23 4.1 Valid Predictive Constructs and the Real...

According to Friston, brain dynamics can be modelled as a large ensemble of coupled nonlinear dynamical subsystems with unstable and transient dynamics. In the present study, two predictions from this model (the existence of nonlinear synchronization between macroscopic field potentials and itinerant nonlinear dynamics) were investigated. The dependence of nonlinearity on the method of measurin...

This contribution presents a new methodology for the optimization based design of uncertain discrete time systems. Constructive nonlinear dynamics methods have been developed for the optimization of dynamical systems under uncertainty over the past few years by the authors [2, 4–8]. The present contribution deals with the extension of these methods to discrete time systems.

I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and “polymorphism”. Using these tools, a uniform linear and non-line...

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to t...