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We investigate the emergence of spatio-temporal patterns in ecological systems. In particular we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predatorprey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 TuringTakens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns is observed.

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socioeconomic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web.

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.

Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Second, we propose to characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown that phase sensitivity appears if there is a nonzero probability for positive local Lyapunov exponents to occur. (c) 1995 American Institute of Physics.

We study the qualitative behavior of a single mechanical rotor with a small amount of damping. This system may possess an arbitrarily large number of coexisting periodic attractors if the damping is small enough. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction, whose boundaries fill almost the whole state space. Most of the attractors observed have low periods, because high period stable orbits generally have basins too small to be detected. We expect the complexity described here to be even more pronounced for higher-dimensional systems, like the double rotor, for which we find more than 1000 coexisting low-period periodic attractors.

Untargeted molecular analyses of complex mixtures are relevant for many fields of research, including geochemistry, pharmacology, and medicine. Ultrahigh-resolution mass spectrometry is one of the most powerful tools in this context. The availability of open scripts and online tools for specific data processing steps such as noise removal or molecular formula assignment is growing, but an integrative tool where all crucial steps are reproducibly evaluated and documented is lacking. We developed a novel, server-based tool (ICBM-OCEAN, Institute for Chemistry and Biology of the Marine Environment, Oldenburg−complex molecular mixtures, evaluation & analysis) that integrates published and novel approaches for standardized processing of ultrahigh-resolution mass spectrometry data of complex molecular mixtures. Different from published approaches, we offer diagnostic and validation tools for all relevant steps. Among other features, we included objective and reproducible reduction of noise and systematic errors, spectra recalibration and alignment, and identification of likeliest molecular formulas. With 15 chemical elements, the tool offers high flexibility in formula attribution. Alignment of mass spectra among different samples prior to molecular formula assignment improves mass error and facilitates molecular formula confirmation with the help of isotopologues. The online tool and the detailed instruction manual are freely accessible at www.icbm.de/icbm-ocean.

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