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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Coherent structure analysis of spatiotemporal chaos.

We introduce a measure to quantify spatiotemporal turbulence in extended systems. It is based on the statistical analysis of a coherent structure decomposition of the evolving system. Applied to a cellular excitable medium and a reaction-diffusion model describing the oxidation of CO on Pt(100), it reveals power-law scaling of the size distribution of coherent space-time structures for the state of spiral turbulence.

Self-segregation of competitive chaotic populations.

The dynamical behavior of species competing for a common resource is studied with a reaction-diffusion system based on cubic autocatalysis. Randomly seeded populations self-segregate to form a complex network of domains separated by distinct interfaces. For chaotic populations in one-dimensional media, the interfaces exhibit irregular motions on long time scales.

Discrimination of irritable bowel syndrome by non-linear analysis of 24-h jejunal motility.

Conventional analysis of ambulatory longterm manometry of the small intestine has revealed abnormalities in patients with the irritable bowel syndrome (IBS). The aim was to use methods from non-linear dynamics, in particular the concepts of symbolic dynamics and entropy, in order to discriminate motility in IBS from healthy subjects. 24-h jejunal motility was recorded in 30 IBS patients and 30 healthy subjects.