arXiv subjects

Henrik Jeldtoft Jensen

Publications and source records attributed to Henrik Jeldtoft Jensen.

At least 73 records · Page 4Linked to original sources

arXiv2009

Delay before synchronization and its role in latency of sensory awareness

Here we show that for coupled-map systems, the length of the transient prior to synchronization is both dependant on the coupling strength and dynamics of connections: systems with fixed connections and with no self-coupling display quasi-instantaneous synchronization. Too strong tendency for synchronization would in terms of brain dynamics be expected to be a pathological case. We relate how the time to synchrony depends on coupling strength and connection dynamics to the latency between neuronal stimulation and conscious awareness. We suggest that this latency can be identified with the delay before a threshold level of synchrony is achieved between distinct regions within the brain, as suggested by recent empirical evidence, in which case the latency can easily be understood as the inevitable delay before such synchrony builds-up. This is demonstrated here through the study of simplistic coupled-map models.

cond-mat.stat-mech↗

arXiv2009

Mutual information in the Tangled Nature Model

We consider the concept of mutual information in ecological networks, and use this idea to analyse the Tangled Nature model of co-evolution. We show that this measure of correlation has two distinct behaviours depending on how we define the network in question: if we consider only the network of viable species this measure increases, whereas for the whole system it decreases. It is suggested that these are complimentary behaviours that show how ecosystems can become both more stable and better adapted.

q-bio.PE↗

arXiv2009

Global and Local Information in Traffic Congestion

A generic network flow model of transport (of relevance to information transport as well as physical transport) is studied under two different control protocols. The first involves information concerning the global state of the network, the second only information about nodes' nearest neighbors. The global protocol allows for a larger external drive before jamming sets in, at the price of significant larger flow fluctuations. By triggering jams in neighboring nodes, the jamming perturbation grows as a pulsating core. This feature explains the different results for the two information protocols.

nlin.AO↗

arXiv2009

Spreading on a complex network avoiding certain motifs

Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not reaching certain sub-classes of the network. We show that excluding nodes and edges from the network has a subtle effect on the percolation. We study two specific examples of degree distributions (exponential and scale free) for which analytical solutions can be obtained. The two cases exhibit qualitatively different behavior.

cond-mat.dis-nn↗

arXiv2008

Accuracy of the cluster-approximation method in a nonequilibrium model

We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and the dimension of the system. Using increasingly large clusters, we use the cluster approximation method to obtain estimates for the critical points in 1+1 dimensions. For the continuous phase transitions only, extrapolations of these approximations show excellent agreement with simulation results. Further, the approximations suggest that, consistent with simulation results, in 1+1 dimensions no first-order phase transitions are observed.

cond-mat.stat-mech↗

arXiv2008

Change in Order of Phase Transitions on Fractal Lattices

We re-examine a population model which exhibits a continuous absorbing phase transition which belongs to directed percolation in 1+1 dimensions and a first order transition in 2+1 dimensions and above. Studying the model on fractal lattices, we examine at what fractal dimension 1<d_f<2, the change in order occurs. As well as commenting on the order of the transitions, we produce estimates for the critical points and, for continuous transitions, some critical exponents.

cond-mat.stat-mech↗

arXiv2007

The prisoners dilemma on a stochastic non-growth network evolution model

We investigate the evolution of cooperation on a non - growth network model with death/birth dynamics. Nodes reproduce under selection for higher payoffs in a prisoners dilemma game played between network neighbours. The mean field characteristics of the model are explored and an attempt is made to understand the size dependent behaviour of the model in terms of fluctuations in the strategy densities. We also briefly comment on the role of strategy mutation in regulating the strategy densties.

q-bio.PE↗

arXiv2007

Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. As well as briefly examining this critical behavior in 2+1 dimensions, we pay particular attention to the cluster geometry. We observe the different cluster structures that form at criticality for the three different types of critical behavior and show that there exists a linear relationship for the probability of survival against initial cluster size at the tricritical point only.

cond-mat.stat-mech↗

arXiv2007

Understanding clustering in type space using field theoretic techniques

The birth/death process with mutation describes the evolution of a population, and displays rich dynamics including clustering and fluctuations. We discuss an analytical `field-theoretical' approach to the birth/death process, using a simple dimensional analysis argument to describe evolution as a `Super-Brownian Motion' in the infinite population limit. The field theory technique provides corrections to this for large but finite population, and an exact description at arbitrary population size. This allows a characterisation of the difference between the evolution of a phenotype, for which strong local clustering is observed, and a genotype for which distributions are more dispersed. We describe the approach with sufficient detail for non-specialists.

q-bio.PE↗

arXiv2007

Complexity, Collective Effects and Modelling of Ecosystems: formation, function and stability

We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions amongst large numbers of components, leading to ecosystems that possess the prototypical characteristics of complex systems. We argue that statistical mechanics is at present the best methodology available to obtain a quantitative description of complex systems, and that ecology is in urgent need of ``integrative'' approaches that are quantitative and non-stationary. We describe examples where combining statistical mechanics and ecology has led to improved ecological modelling and, at the same time, broadened the scope of statistical mechanics.

q-bio.PE↗

arXiv2007

Using a phase space cross section to study large complex systems

For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce the phase space by defining a phase space cross section. The method is applied to a system of dynamically coupled maps introduced by Ito & Kaneko (Phys. Rev. Lett., 88, 028701, 2001 & Phys. Rev. E, 67, 046226, 2003). We show that the transitions between phases of different synchronization behaviour are not always sharp but can be characterized by fractal boundaries in both phase and parameter space.

cond-mat.stat-mech↗

arXiv2007

Sensitivity of Global Dynamics on the microscopic details of a network of dynamically coupled maps

Here we analyze the behavior of dynamically coupled maps, based on those introduced in a series of papers by Ito and Kaneko (Phys. Rev. Lett. 88:028701, 2002 and Phys. Rev. E 67:046226, 2003). We show how the microscopic coupling mechanism changes the behavior of the system both by affecting the stability of fixed points and through a more subtle effect in the crossover behavior between different regions of the parameter space. This makes it necessary to choose very carefully the exact manner in which one couples maps if they are to be used as a general model of composite systems.

cond-mat.stat-mech↗

arXiv2007

Neutral Evolution as Diffusion in phenotype space: reproduction with mutation but without selection

The process of `Evolutionary Diffusion', i.e. reproduction with local mutation but without selection in a biological population, resembles standard Diffusion in many ways. However, Evolutionary Diffusion allows the formation of local peaks with a characteristic width that undergo drift, even in the infinite population limit. We analytically calculate the mean peak width and the effective random walk step size, and obtain the distribution of the peak width which has a power law tail. We find that independent local mutations act as a diffusion of interacting particles with increased stepsize.

q-bio.PE↗

arXiv2006

Phase transitions in a lattice population model

We introduce a model for a population on a lattice with diffusion and birth/death according to 2A->3A and A->0 for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in 1+1 dimensions and of first-order in higher dimensions in agreement with the mean field equation. For the 1+1 dimensional case, we examine the critical exponents and a scaling function for the survival probability and show that it belongs to the universality class of directed percolation. In higher dimensions, we look at the first-order phase transition by plotting a histogram of the population density and use the presence of phase coexistence to find an accurate value for the critical point in 2+1 dimensions.

cond-mat.stat-mech↗

arXiv2006

Allee Effects and Extinction in a Lattice Model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which extinction is assured. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.

q-bio.PE↗

arXiv2006

The species-area relationship and evolution

Models relating to the Species-Area curve are usually defined at the species level, and concerned only with ecological timescales. We examine an individual-based model of co-evolution on a spatial lattice based on the Tangled Nature model, and show that reproduction, mutation and dispersion by diffusion in an interacting system produces power-law Species-Area Relations as observed in ecological measurements at medium scales. We find that co-evolutionary habitats form, allowing high diversity levels in a spatially homogenous system, and these are maintained for exponentially increasing time when increasing system size.

q-bio.PE↗

arXiv2006

Correlation, selection and the evolution of species networks

We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction networks with exponential degree distributions and an inverse dependence between connectance and species richness. We use a simplified network evolution model to demonstrate that the observed degree distributions can occur as a consequence of partial correlations in the inheritance process. Futher to this, in the limit of low connectance and maximal correlation, distributions of power law form, $P(k){\propto}1/k$, can be achieved. We also show that a hyperbolic relationship between connectance and species richness, $C{\sim}1/D$ can arise as a consequence of probabilistic constraints on the evolutionary search process.

q-bio.PE↗

arXiv2006

A steady state network model with a 1/k scale-free degree distribution

Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential attachment is counterbalanced by preferential detachment. The mean field evolution is considered and the 1/k law is verified under certain approximations. An ansatz for the degree distribution is proposed on the basis of symmetry considerations and is shown to coincide well with the simulation data. Distributional forms other than power law are also shown to arise when the condition of perfect duplication is relaxed.

cond-mat.stat-mech↗