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At least 1,711 records · Page 95Linked to original sources
PubMed2001

Reconstruction of chaotic dynamics by on-line EM algorithm.

In this paper, we discuss the reconstruction of chaotic dynamics by using a normalized Gaussian network (NGnet), which is a network of local linear regression units. The NGnet is trained by an on-line EM algorithm in order to learn the vector field of the chaotic dynamics. We investigate the robustness of our approach to two kinds of noise processes: system noise and observation noise. System noise disturbs the system dynamics itself. Observation noise is added when the state variables are observed. It is shown that the trained NGnet is able to reproduce a chaotic attractor, which approximates the complexity and instability of the original chaotic attractor well, even under various noise conditions. The trained NGnet also shows good prediction performance. When only part of the dynamical variables are observed, the delay embedding method is used. The NGnet is then trained to learn the vector field in the delay coordinate space. Experiments show that the chaotic dynamics embedded in the delay coordinate space is able to be learned under the two types of noise.

Algorithms↗
PubMed2002

A theoretical framework of ecological phase transitions for characterizing tree-grass dynamics.

This paper describes a theoretical framework of ecological phase transitions for modeling tree-grass dynamics and analyzing the shifts or phase transitions from one vegetation structure to another in the southern Texas landscape. This framework implements the integration of percolation theory, fractal geometry and phase transition theory as a method for modeling the spatial patterns of tree-grass dynamics, and nonlinear Markov non-equilibrium thermodynamic stability theory as a method for characterizing temporal tree-grass dynamics and phase transition. An historical sequence of aerial photographs at a Prosopis-thornscrub savanna parkland site in southern Texas was used to determine the parameters of the models. The preliminary analytical result accords well with current understanding and field survey of vegetation dynamics in the southern Texas landscape. The potential of such approaches and other relevant theories such as self-organized criticality and synergetics to vegetation dynamics is also discussed.

Ecosystem↗
PubMedDate not supplied

A novel method for the topographic analysis of neural activity reveals formation and dissolution of 'Dynamic Cell Assemblies'.

The study of synchronous oscillations in neural systems is a very active area of research. However, cognitive function may depend more crucially upon a dynamic alternation between synchronous and desynchronous activity rather than synchronous behaviour per se. The principle aim of this study is to develop and validate a novel method of quantifying this complex process. The method permits a direct mapping of phase synchronous dynamics and desynchronizing bursts in the spatial and temporal domains. Two data sets are analyzed: Numeric data from a model of a sparsely coupled neural cell assembly and experimental data consisting of scalp-recorded EEG from 40 human subjects. In the numeric data, the approach enables the demonstration of complex relationships between cluster size and temporal duration that cannot be detected with other methods. Dynamic patterns of phase-clustering and desynchronization are also demonstrated in the experimental data. It is further shown that in a significant proportion of the recordings, the pattern of dynamics exhibits nonlinear structure. We argue that this procedure provides a 'natural partitioning' of ongoing brain dynamics into topographically distinct synchronous epochs which may be integral to the brain's adaptive function. In particular, the character of transitions between consecutive synchronous epochs may reflect important aspects of information processing and cognitive flexibility.

Adaptation, Ocular↗
PubMed2006

The dynamics of perception and action.

How might one account for the organization in behavior without attributing it to an internal control structure? The present article develops a theoretical framework called behavioral dynamics that integrates an information-based approach to perception with a dynamical systems approach to action. For a given task, the agent and its environment are treated as a pair of dynamical systems that are coupled mechanically and informationally. Their interactions give rise to the behavioral dynamics, a vector field with attractors that correspond to stable task solutions, repellers that correspond to avoided states, and bifurcations that correspond to behavioral transitions. The framework is used to develop theories of several tasks in which a human agent interacts with the physical environment, including bouncing a ball on a racquet, balancing an object, braking a vehicle, and guiding locomotion. Stable, adaptive behavior emerges from the dynamics of the interaction between a structured environment and an agent with simple control laws, under physical and informational constraints.

Animals↗
PubMed1994

Analysis of vocal disorders with methods from nonlinear dynamics.

Several authors have recently demonstrated the intimate relationship between nonlinear dynamics and observations in vocal fold vibration (Herzel, 1993; Mende, Herzel, & Wermke, 1990; Titze, Baken, & Herzel, 1993). The aim of this paper is to analyze vocal disorders from a nonlinear dynamics point of view. Basic concepts and analysis techniques from nonlinear dynamics are reviewed and related to voice. The voices of several patients with vocal disorders are analyzed using traditional voice analysis techniques and methods from nonlinear dynamics. The two methods are shown to complement each other in many ways. Likely physiological mechanisms of the observed nonlinear phenomena are presented, and it is shown how much of the terminology in the literature describing rough voice can be unified within the framework of nonlinear dynamics.

Electroencephalography↗
PubMed2003

A challenge to chaotic itinerancy from brain dynamics.

Brain hermeneutics and chaotic itinerancy proposed by Tsuda are attractive characterizations of perceptual dynamics in the mammalian olfactory system. This theory proposes that perception occurs at the interface between itinerant neural representation and interaction with the environment. Quantifiable application of these dynamics has been hampered by the lack of definable history and action processes which characterize the changes induced by behavioral state, attention, and learning. Local field potentials measured from several brain areas were used to characterize dynamic activity patterns for their use as representations of history and action processes. The signals were recorded from olfactory areas (olfactory bulb, OB, and pyriform cortex) and hippocampal areas (entorhinal cortex and dentate gyrus, DG) in the brains of rats. During odor-guided behavior the system shows dynamics at three temporal scales. Short time-scale changes are system-wide and can occur in the space of a single sniff. They are predictable, associated with learned shifts in behavioral state and occur periodically on the scale of the intertrial interval. These changes occupy the theta (2-12 Hz), beta (15-30 Hz), and gamma (40-100 Hz) frequency bands within and between all areas. Medium time-scale changes occur relatively unpredictably, manifesting in these data as alterations in connection strength between the OB and DG. These changes are strongly correlated with performance in associated trial blocks (5-10 min) and may be due to fluctuations in attention, mood, or amount of reward received. Long time-scale changes are likely related to learning or decline due to aging or disease. These may be modeled as slow monotonic processes that occur within or across days or even weeks or years. The folding of different time scales is proposed as a mechanism for chaotic itinerancy, represented by dynamic processes instead of static connection strengths. Thus, the individual maintains continuity of experience within the stability of fast periodic and slow monotonic processes, while medium scale events alter experience and performance dramatically but temporarily. These processes together with as yet to be determined action effects from motor system feedback are proposed as an instantiation of brain hermeneutics and chaotic itinerancy.

Animals↗
PubMed2004

Random dynamics of the Morris-Lecar neural model.

Determining the response characteristics of neurons to fluctuating noise-like inputs similar to realistic stimuli is essential for understanding neuronal coding. This study addresses this issue by providing a random dynamical system analysis of the Morris-Lecar neural model driven by a white Gaussian noise current. Depending on parameter selections, the deterministic Morris-Lecar model can be considered as a canonical prototype for widely encountered classes of neuronal membranes, referred to as class I and class II membranes. In both the transitions from excitable to oscillating regimes are associated with different bifurcation scenarios. This work examines how random perturbations affect these two bifurcation scenarios. It is first numerically shown that the Morris-Lecar model driven by white Gaussian noise current tends to have a unique stationary distribution in the phase space. Numerical evaluations also reveal quantitative and qualitative changes in this distribution in the vicinity of the bifurcations of the deterministic system. However, these changes notwithstanding, our numerical simulations show that the Lyapunov exponents of the system remain negative in these parameter regions, indicating that no dynamical stochastic bifurcations take place. Moreover, our numerical simulations confirm that, regardless of the asymptotic dynamics of the deterministic system, the random Morris-Lecar model stabilizes at a unique stationary stochastic process. In terms of random dynamical system theory, our analysis shows that additive noise destroys the above-mentioned bifurcation sequences that characterize class I and class II regimes in the Morris-Lecar model. The interpretation of this result in terms of neuronal coding is that, despite the differences in the deterministic dynamics of class I and class II membranes, their responses to noise-like stimuli present a reliable feature.

Animals↗
PubMed2003

Spatial dynamics in model plant communities: what do we really know?

A variety of models have shown that spatial dynamics and small-scale endogenous heterogeneity (e.g., forest gaps or local resource depletion zones) can change the rate and outcome of competition in communities of plants or other sessile organisms. However, the theory appears complicated and hard to connect to real systems. We synthesize results from three different kinds of models: interacting particle systems, moment equations for spatial point processes, and metapopulation or patch models. Studies using all three frameworks agree that spatial dynamics need not enhance coexistence nor slow down dynamics; their effects depend on the underlying competitive interactions in the community. When similar species would coexist in a nonspatial habitat, endogenous spatial structure inhibits coexistence and slows dynamics. When a dominant species disperses poorly and the weaker species has higher fecundity or better dispersal, competition-colonization trade-offs enhance coexistence. Even when species have equal dispersal and per-generation fecundity, spatial successional niches where the weaker and faster-growing species can rapidly exploit ephemeral local resources can enhance coexistence. When interspecific competition is strong, spatial dynamics reduce founder control at large scales and short dispersal becomes advantageous. We describe a series of empirical tests to detect and distinguish among the suggested scenarios.

Ecosystem↗
PubMed2003

Patterns of dispersal and dynamics among habitat patches varying in quality.

Both source-sink theory and extensions of optimal foraging theory ("balanced dispersal" theory) address dispersal and population dynamics in landscapes where habitat patches vary in quality. However, studying dispersal mechanisms empirically has proven difficult, and dispersal is rarely tied back to long-term spatial dynamics. We used a manipulable laboratory system consisting of bacteria and protozoa to investigate the ability of source-sink and optimal foraging theories to explain both dispersal and emergent spatial dynamics. Consistent with source-sink models and contrary to balanced dispersal models, there was a consistent net flux of protist individuals from high to low resource patches. However, unlike the simplest source-sink models, intermediate rates of dispersal led to highest abundances in low resource patches. Side experiments found strong density dependence in local population dynamics and differences in average protist body size in high and low resource patches. Parameterization and analysis of a two-patch model showed that high migration from high to low resource patches could have depressed population density in low resource patches, creating pseudosinks. The movement of individuals and biomass from sources to sinks (a form of ecosystem subsidy) resulted in the convergence of body size and population densities in sources and sinks. Our results indicate a need to carefully consider movement patterns and interaction with local dynamics in potential source-sink systems.

Animals↗
PubMed2004

Dynamics of compartmented and reticulate food webs in relation to energetic flows.

Using simple food webs, we address how the interactions of food web structure and energetic flows influence dynamics. We examine the effect of food web topologies with equivalent energetics (i.e., trophic interactions are equivalent at each trophic level), following which we vary energetic flows to include weak and strong interactions or nonequivalent energetics. In contrast to some work (Pimm 1979), we find that compartmented webs are more stable than reticulate webs. However, we find that nonequivalent energetics can stabilize previously unstable reticulate structures. It is not only weak flows that can be stabilizing but also the arrangement of the flows that emphasizes stabilizing mechanisms. We find that the main stabilizing mechanism is asynchrony, where structures and energetic arrangements that decrease synchrony such as internal segregation or competition will stabilize dynamics. Since compartments allow prey dynamics to behave somewhat independently, compartmentation readily promotes stability. In addition, these results can be scaled from simple food webs to more complex webs with many interacting subsystems so that linking weak subsystems to strong ones can stabilize dynamics. We show that food web dynamics are determined not only by topology but also the arrangement of weak and strong energetic flows.

Animals↗
PubMed1998

Dynamics of a feline retrovirus (FeLV) in host populations with variable spatial structure.

The predictions of epidemic models are remarkably affected by the underlying assumptions concerning host population dynamics and the relation between host density and disease transmission. Furthermore, hypotheses underlying distinct models are rarely tested. Domestic cats (Felis catus) can be used to compare models and test their predictions, because cat populations show variable spatial structure that probably results in variability in the relation between density and disease transmission. Cat populations also exhibit various dynamics. We compare four epidemiological models of Feline Leukaemia Virus (FeLV). We use two different incidence terms, i.e. proportionate mixing and pseudo-mass action. Population dynamics are modelled as logistic or exponential growth. Compared with proportionate mixing, mass action incidence with logistic growth results in a threshold population size under which the virus cannot persist in the population. Exponential growth of host populations results in systems where FeLV persistence at a steady prevalence and depression of host population growth are biologically unlikely to occur. Predictions of our models account for presently available data on FeLV dynamics in various populations of cats. Thus, host population dynamics and spatial structure can be determinant parameters in parasite transmission, host population depression, and disease control.

Animals↗
PubMed2002

Dynamics of a mutualism in a multi-species context.

Despite recent findings that mutualistic interactions between two species may be greatly affected by species external to the mutualism, the implications of such multi-species interactions for the population dynamics of the mutualists are virtually unexplored. In this paper, we ask how the mutualism between the shoot-base boring weevil Apion onopordi and the rust fungus Puccinia punctiformis is influenced by the dynamics of their shared host plant Cirsium arvense, and vice versa. In particular, we hypothesized that the distribution of the weevil's egg load between healthy and rust-infected thistles may regulate the abundance of the mutualists and their host plant. In contrast to our expectations we found that the dynamics of the mutualists are largely determined by the dynamics of their host. This is, to our knowledge, the first demonstration that the dynamics of a mutualism are driven by a third, non-mutualistic species.

Animals↗
PubMed2004

Predicting shifts in dynamics of cannibalistic field populations using individual-based models.

The occurrence of qualitative shifts in population dynamical regimes has long been the focus of population biologists. Nonlinear ecological models predict that these shifts in dynamical regimes may occur as a result of parameter shifts, but unambiguous empirical evidence is largely restricted to laboratory populations. We used an individual-based modelling approach to predict dynamical shifts in field fish populations where the capacity to cannibalize differed between species. Model-generated individual growth trajectories that reflect different population dynamics were confronted with empirically observed growth trajectories, showing that our ordering and quantitative estimates of the different cannibalistic species in terms of life-history characteristics led to correct qualitative predictions of their dynamics.

Animals↗
PubMed2005

Changes in maternal investment in eggs can affect population dynamics.

The way that mothers provision their offspring can have important consequences for their offspring's performance throughout life. Models suggest that maternally induced variation in life histories may have large population dynamical effects, even perhaps driving cycles such as those seen in forest Lepidoptera. The evidence for large maternal influences on population dynamics is unconvincing, principally because of the difficulty of conducting experiments at both the individual and population level. In the soil mite, Sancassania berlesei, we show that there is a trade-off between a female's fecundity and the per-egg provisioning of protein. The mother's position on this trade-off depends on her current food availability and her age. Populations initiated with 250 eggs of different mean sizes showed significant differences in the population dynamics, converging only after three generations. Differences in the growth, maturation and fecundity of the initial cohort caused differences in the competitive environment for the next generation, which, in turn, created differences in their growth and reproduction. Maternal effects in one generation can therefore lead to population dynamical consequences over many generations. Where animals live in environments that are temporally variable, we conjecture that maternal effects could result in long-term dynamical effects.

Animal Nutritional Physiological Phenomena↗
PubMed1996

State-dependent life history evolution in Soay sheep: dynamic modelling of reproductive scheduling.

Adaptive decisions concerning the scheduling of reproduction in an animal's lifetime, including age at maturity and clutch or litter size, should depend on an animal's body condition or state. In this state-dependent case, we are concerned with the optimization of sequences of actions and so dynamic optimization techniques are appropriate. Here we show how stochastic dynamic programming can be used to study the reproductive strategies and population dynamics of natural populations, assuming optimal decisions. As examples we describe models based upon field data from an island population of Soay sheep on St. Kilda. This population shows persistent instability, with cycles culminating in high mortality every three or four years. We explore different assumptions about the extent to which Soay ewes use information about the population cycle in making adaptive decisions. We compare the observed distributions of strategies and population dynamics with model predictions; the results indicate that Soay ewes make optimal reproductive decisions given that they have no information about the population cycle. This study represents the first use of a dynamic optimization life history model of realistic complexity in the study of a field population. The techniques we use are potentially applicable to many other populations, and we discuss their extension to other species and other life history questions.

Acclimatization↗
PubMed2006

Nonlinear dynamics and self-organization of rotary molecular motor ensembles.

The coupled nonlinear dynamics of rotary motor ensembles and an embedding fluid medium are simulated on the basis of Navier-Stokes equations. The model description considers space-dependent rotation of motors and a spatially inhomogeneous motor distribution as well as spatial fluctuations in molecular properties. The mutual influence of motor rotations and fluid dynamics as well as spatial inhomogeneities of their molecular properties are self-consistently included. Space-time simulations visualize the complex interplay between the fluid dynamics and motor rotation and show that the dynamic coupling to the environment via the velocity field as well as the spatial inhomogeneity and distribution of rotors determines the overall behavior of the motor complex. Depending on the initial molecular distribution, rotation frequency, and fluid dynamics a spatial self-organization or a chaotic behavior may arise.

Computer Simulation↗
PubMed2005

Coevolutionary dynamics: from finite to infinite populations.

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.

Animals↗
PubMed2004

A network of coincidence detector neurons with periodic and chaotic dynamics.

We propose a simple neural network model to understand the dynamics of temporal pulse coding. The model is composed of coincidence-detector neurons with uniform synaptic efficacies and random pulse propagation delays. We also assume a global negative feedback mechanism which controls the network activity, leading to a fixed number of neurons firing within a certain time window. Due to this constraint, the network state becomes well defined and the dynamics equivalent to a piecewise nonlinear map. Numerical simulations of the model indicate that the latency of neuronal firing is crucial to the global network dynamics; when the timing of postsynaptic firing is less sensitive to perturbations in timing of presynaptic spikes, the network dynamics become stable and periodic, whereas increased sensitivity leads to instability and chaotic dynamics. Furthermore, we introduce a learning rule which decreases the Lyapunov exponent of an attractor and enlarges the basin of attraction.

Action Potentials↗