Biomedical subjects

Ulrike Feudel

Publications and source records attributed to Ulrike Feudel.

12 recordsLinked to original sources

PubMed2006

Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations.

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 predator-prey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 Turing-Takens-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, are observed.

Animals↗

PubMed2006

Generalized models as a universal approach to the analysis of nonlinear dynamical systems.

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.

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PubMed2005

Basin bifurcations in quasiperiodically forced coupled systems.

We study the effect of quasiperiodic forcing on a system of coupled identical logistic maps. Upon a variation of system parameters, a variety of different dynamical regimes can be observed, including phenomena such as bistability and multistability. At the bifurcation to bistability, in a manner reminiscent of attractor expansion at interior crises, there is an abrupt change in the size of attractor basins. In the bistable region, attractor basins undergo additional bifurcations wherein holes and islands are created within the basins when system parameters change. These can be understood by examining critical surfaces for the coupled system.

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PubMed2004

Enrichment and foodchain stability: the impact of different forms of predator-prey interaction.

We propose a simple model of an ecological foodchain of arbitrary length. The model is very general in nature and describes a whole class of foodchains. Using the methods of qualitative analysis the model's stability can be analysed without restricting the predator-prey interaction to any specific functional form. The model can therefore be used to study the effect of different functional forms on the stability of the foodchain. We demonstrate that the stability of steady states may strongly depend on the exact functional form of the interaction function used. It is shown that a class of interaction functions exists, which are similar to the widely used Holling functions but bestow radically different stability properties upon the model. An example is shown in which enrichment has a stabilizing effect on the foodchain. By contrast enrichment destabilizes steady states if Holling functions are used.

Animals↗

PubMed2003

Why are chaotic attractors rare in multistable systems?

We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.

Models, Theoretical↗

PubMed2003

Synchronization and desynchronization under the influence of quasiperiodic forcing.

We study the influence of quasiperiodic forcing on synchronization and desynchronization using two coupled quasiperiodically forced logistic maps as a paradigm. We show that due to the forcing the synchronization region in parameter space shrinks. The loss of transverse stability of the synchronized attractors leads to desynchronization. Two types of such blowout bifurcations are described, namely, the blowout bifurcations of synchronized quasiperiodic motion on invariant curves and synchronized strange nonchaotic attractors, both yielding desynchronized chaotic attractors.

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PubMed2003

Enhancement of noise-induced escape through the existence of a chaotic saddle.

We study the noise-induced escape process in a prototype dissipative nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle embedded in the basin of attraction of the metastable state, we find the novel phenomenon of a strong enhancement of noise-induced escape. This result is established by employing the theory of quasipotentials. Our finding is of general validity and should be experimentally observable.

Journal Article↗

PubMed2002

Multistability, noise, and attractor hopping: the crucial role of chaotic saddles.

We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect is explained by a bifurcation involving two chaotic saddles. We also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis.

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PubMed2002

Bifurcations of a semiclassical atom in a periodic field.

The dynamics of an electron moving in the Coulomb field of a nucleus and a strong periodic field is studied in a semiclassical model. Hamiltonian equations of motion are derived using Gaussian wave functions, a variational principle, and an adiabatic approximation for the width of the wave packets. Predictions for the ionization probability are found to agree rather well with exact calculations in the barrier suppression regime. By introducing dissipation and fluctuation the model atom is considered as an open system. For the dissipative system we investigate the bifurcations in dependence on strength and frequency of the external field. A quite complex bifurcation scenario is obtained. The sensitivity with respect to noise is also studied.

Journal Article↗

PubMed2000

Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons.

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.

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PubMed1997

Multistability and the control of complexity.

We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (c) 1997 American Institute of Physics.

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PubMed1995

Characterizing strange nonchaotic attractors.

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.

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