How realistic features affect the stability of an Arctic marine food web model.

Rapid sea-ice decline and warmer waters are threatening the stability of Arctic ecosystems and potentially forcing their restructuring. Mathematical models that support observational evidence are becoming increasingly important. We develop a food web model for the Southern Beaufort Sea based on species with high ecological significance. Generalized modeling is applied to study the impact of realistic characteristics on food web stability; a powerful method that provides a linear stability analysis for systems with uncertainty in data and underlying physical processes. We find that including predator-specific foraging traits, weighted predator-prey interactions, and habitat constraints increase food-web stability. The absence of a fierce top predator (killer whale, polar bear, etc.) also significantly increases the portion of stable webs. Adding ecosystem background noise in terms of a collective impact of latent, minor ecosystem members shows a peak in stability at an optimum, relatively small background pressure. These results indicate that refining models with more realistic detail to account for the complexity of the ecological system may be key to bridge the gap between empirical observations and model predictions in ecosystem stability.

Combining generalized modeling and specific modeling in the analysis of ecological networks.

The complexity of real food webs involves uncertainty in data and in underlying ecological processes, and modeling approaches deal with these challenges differently. Generalized modeling provides a linear stability analysis without narrow specification of all processes, and conventional dynamical systems models approximate functional forms to discuss trajectories in phase space. This study compares results and ecological interpretations from both methods in four-species ecological networks at steady state. We find that a specific (dynamical systems) model only provides a subset of stability data from the generalized model, which spans many plausible dynamic scenarios, allowing for conflicting results. Nevertheless, both approaches reveal that fixed points become stable when nutrient flows to predators are fettered and even more when the basal growth rate approaches a maximum. The specific model identifies a distinct ecosystem response to bottom-up forcing, the enrichment of lower trophic levels. Enrichment stabilizes a fixed point when basal species are in a resource-deprived environment but destabilizes it if resources become more abundant. The generalized model provides less specific information since infinitely many paths of enrichment are hypothetical. Nevertheless, generalized modeling of ecological systems is a powerful technique that enables a meta analysis of these uncertain complex systems.

Stability of generalized ecological-network models.

The stability of ecological networks of varying topologies and predator-prey relationships is explored by applying the concept of generalized modeling. The effects of omnivory, complexity, enrichment, number of top predators, and predatory response are discussed. The degree of omnivory plays a large role in governing web stability at steady state. Complexity as measured from connectance and network size is not a perfect indicator of stability; large, highly connected webs can be just as stable as smaller, less connected ones. Learning behavior as expressed in Holling's type III predatory response is stabilizing for food webs and provides exceptions to the paradox of enrichment for some topologies.

Alternating activity patterns and a chimeralike state in a network of globally coupled excitable Morris-Lecar neurons.

Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.

Transient chaos and associated system-intrinsic switching of spacetime patterns in two synaptically coupled layers of Morris-Lecar neurons.

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a single layer of diffusively coupled, excitable Morris-Lecar neurons. Weak synaptic coupling of two such layers reveals system intrinsic switching of spatiotemporal activity patterns within and between the layers at irregular times. Within a layer, switching sequences include spatiotemporal chaos, erratic and regular pulse propagation, spontaneous network wide neuron activity, and rest state. A momentary substantial reduction in neuron activity in one layer can reinitiate transient spatiotemporal chaos in the other layer, which can induce a swap of spatiotemporal chaos with a pulse state between the layers. Presynaptic input maximizes the distance between propagating pulses, in contrast to pulse merging in the absence of synapses.

Impact of weak excitatory synapses on chaotic transients in a diffusively coupled Morris-Lecar neuronal network.

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state.

Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.

Length scale of interaction in spatiotemporal chaos.

Extensive systems have no long scale correlations and behave as a sum of their parts. Various techniques are introduced to determine a characteristic length scale of interaction beyond which spatiotemporal chaos is extensive in reaction-diffusion networks. Information about network size, boundary condition, or abnormalities in network topology gets scrambled in spatiotemporal chaos, and the attenuation of information provides such characteristic length scales. Space-time information flow associated with the recovery of spatiotemporal chaos from finite perturbations, a concept somewhat opposite to the paradigm of Lyapunov exponents, defines another characteristic length scale. High-precision computational studies of asymptotic spatiotemporal chaos in the complex Ginzburg-Landau system and transient spatiotemporal chaos in the Gray-Scott network show that these different length scales are comparable and thus suitable to define a length scale of interaction. Preliminary studies demonstrate the relevance of these length scales for stable chaos.

Regular network model for the sea ice-albedo feedback in the Arctic.

The Arctic Ocean and sea ice form a feedback system that plays an important role in the global climate. The complexity of highly parameterized global circulation (climate) models makes it very difficult to assess feedback processes in climate without the concurrent use of simple models where the physics is understood. We introduce a two-dimensional energy-based regular network model to investigate feedback processes in an Arctic ice-ocean layer. The model includes the nonlinear aspect of the ice-water phase transition, a nonlinear diffusive energy transport within a heterogeneous ice-ocean lattice, and spatiotemporal atmospheric and oceanic forcing at the surfaces. First results for a horizontally homogeneous ice-ocean layer show bistability and related hysteresis between perennial ice and perennial open water for varying atmospheric heat influx. Seasonal ice cover exists as a transient phenomenon. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice.

Transient spatiotemporal chaos is extensive in three reaction-diffusion networks.

Extensive (asymptotic) spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly. A systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction-diffusion networks for various boundary conditions. The Lyapunov dimension, the sum of positive Lyapunov exponents, and the logarithm of the transient lifetime grow linearly with the system size. The unstable manifold of the chaotic saddle has nearly the same dimension as the saddle itself, and the stable manifold is nearly space filling.

Noise can delay and advance the collapse of spatiotemporal chaos.

Spatiotemporal chaos on a regular ring network of excitable Gray-Scott dynamical elements collapses to a stable asymptotic state. We find that the addition of dynamical noise clearly influences the spatiotemporal pattern and the transient lifetime of spatiotemporal chaos. Spatially uniform noise significantly decreases the average lifetime of spatiotemporal chaos due to an enlargement of regions of local collapse. For spatially inhomogeneous noise the collapse is maximally delayed at an intermediate noise level, but drastically advanced for larger noise levels.

Master stability analysis in transient spatiotemporal chaos.

The asymptotic stability of spatiotemporal chaos is difficult to determine, since transient spatiotemporal chaos may be extremely long lived. A master stability analysis reveals that the asymptotic state of transient spatiotemporal chaos in the Gray-Scott system and in the Bär-Eiswirth system is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime of transient spatiotemporal chaos depends on the number of transverse directions that are unstable along a typical excitation cycle.

Nonlocal coupling can prevent the collapse of spatiotemporal chaos.

Spatiotemporal chaos on a regular ring network of excitable Gray-Scott dynamical elements is transient. We find that the addition of very few nonlocal network connections drastically changes the average lifetime of spatiotemporal chaos. In the presence of a single shortcut local interface formation delays the collapse of spatiotemporal chaos. This competes with a reduced average characteristic path length that advances the collapse process. Two added shortcuts can prevent the collapse of spatiotemporal chaos by causing an asymptotic local collapse.

Collapse of spatiotemporal chaos.

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.

Topographic organization of Hebbian neural connections by synchronous wave activity.

Experimental studies have revealed that the refinement of early, imprecise connections in the developing visual system involves activity in the retina before the onset of vision. We study the evolution of initially random unidirectional connections between two excitable layers of FitzHugh-Nagumo neurons with simulated spontaneous activity in the input layer. Lateral coupling within the layers yields synchronous neural wave activity that serves as a template for the Hebbian learning process, which establishes topographically precise interlayer connections. (c) 2001 American Institute of Physics.

Symbolic dynamics of jejunal motility in the irritable bowel.

Different studies of the irritable bowel syndrome (IBS) by conventional analysis of jejunal motility report conflicting results. Therefore, our aim is to quantify the jejunal contraction activity by symbolic dynamics in order to discriminate between IBS and control subjects. Contraction amplitudes during fasting motility (phase II) are analyzed for 30 IBS and 30 healthy subjects. On the basis of a particular scale-independent discretization of the contraction amplitudes with respect to the median, IBS patients are characterized by increased block entropy as well as increased mean contraction amplitude. In a further more elementary level of analysis these differences can be reduced to specific contraction patterns within the time series, namely the fact that successive large contraction amplitudes are less ordered in IBS than in controls. These significant differences in jejunal motility may point to an altered control of the gut in IBS, although further studies on a representative number of patients have to be done for a validation of these findings. (c) 1999 American Institute of Physics.