The interdisciplinary field of nonlinear chemical dynamics has grown significantly in breadth and depth over the past three decades. Its subject matter and applications encompass all branches of chemistry as well as areas of mathematics, physics, biology and engineering. In this Perspective, we present an overview of some of the key results of nonlinear chemical dynamics, with emphasis on those...

Earthquake faults occur in networks that have dynamical modes not displayed by single isolated faults. Using simulations of the network of strike-slip faults in southern California, we find that the physics depends critically on both the interactions among the faults, which are determined by the geometry of the fault network, as well as on the stress dissipation properties of the nonlinear fric...

This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas ± cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on wo...

Throughout much of ecology’s history, most ecologists have believed that ecological systems tend towards an equilibrium – a notion popularized as ‘the balance of nature’ – and that deviations from that equilibrium are caused by external perturbations. By assuming that systemswere close to equilibrium, ecologists coulddescribe them with linear models that were mathematically tractable. However, ...

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution fun...

In the last few decades, theory of dynamical systems has become a rapidly growing area of mathematics and attracted many researchers. This theory is an important and wellestablished branch of the modern mathematics. The reason lies in the fact that the study of dynamical systems not only has an important theoretical interest, but also is motivated by problems from other disciplines, including p...

Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is ...

This paper introduces the Global-Local Mapping Approximation algorithm as a candidate for identifying nonlinear, six degree-of-freedom rigid body aircraft dynamics. The technique models the nonlinear dynamical model as a sum of linear model and nonlinear model. The linear model dynamics are assumed to be perturbed by a nonlinear term which represents the system nonlinearities that are not captu...

In this article, a new approach based on blockoriented nonlinear models for modeling and identification of aircraft nonlinear dynamics has been proposed. Some of the block-oriented nonlinear models are considered as flexible structures which are suitable for the identification of widely applicable dynamic systems. These models are able to approximate a wide range of system dynamics. Flying vehi...