Statistics of extinction and survival in Lotka-Volterra systems

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.Comment: Previous version had error in authors. 11 pages, including 5 figure

Self-organized criticality in deterministic systems with disorder

Using the Bak-Sneppen model of biological evolution as our paradigm, we investigate in which cases noise can be substituted with a deterministic signal without destroying Self-Organized Criticality (SOC). If the deterministic signal is chaotic the universality class is preserved; some non-universal features, such as the threshold, depend on the time correlation of the signal. We also show that, if the signal introduced is periodic, SOC is preserved but in a different universality class, as long as the spectrum of frequencies is broad enough.Comment: RevTex, 8 pages, 8 figure

Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks

The aim of the study was to compare the epidemic spread on static and dynamic small-world networks. The network was constructed as a 2-dimensional Watts-Strogatz model (500x500 square lattice with additional shortcuts), and the dynamics involved rewiring shortcuts in every time step of the epidemic spread. The model of the epidemic is SIR with latency time of 3 time steps. The behaviour of the epidemic was checked over the range of shortcut probability per underlying bond 0-0.5. The quantity of interest was percolation threshold for the epidemic spread, for which numerical results were checked against an approximate analytical model. We find a significant lowering of percolation thresholds for the dynamic network in the parameter range given. The result shows that the behaviour of the epidemic on dynamic network is that of a static small world with the number of shortcuts increased by 20.7 +/- 1.4%, while the overall qualitative behaviour stays the same. We derive corrections to the analytical model which account for the effect. For both dynamic and static small-world we observe suppression of the average epidemic size dependence on network size in comparison with finite-size scaling known for regular lattice. We also study the effect of dynamics for several rewiring rates relative to latency time of the disease.Comment: 13 pages, 6 figure

Switching model with two habitats and a predator involving group defence

Switching model with one predator and two prey species is considered. The prey species have the ability of group defence. Therefore, the predator will be attracted towards that habitat where prey are less in number. The stability analysis is carried out for two equilibrium values. The theoretical results are compared with the numerical results for a set of values. The Hopf bifuracation analysis is done to support the stability results

Eroding market stability by proliferation of financial instruments

We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the development of financial instruments, with a dynamical picture of an interacting market, in a simple setting. The proliferation of financial instruments apparently provides more means for risk diversification, making the market more efficient and complete. In the simple market of interacting traders discussed here, the proliferation of financial instruments erodes systemic stability and it drives the market to a critical state characterized by large susceptibility, strong fluctuations and enhanced correlations among risks. This suggests that the hypothesis of APT may not be compatible with a stable market dynamics. In this perspective, market stability acquires the properties of a common good, which suggests that appropriate measures should be introduced in derivative markets, to preserve stability.Comment: 26 pages, 8 figure

From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200

Iterated maps for clarinet-like systems

The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime for string instruments. In this article, we study in more detail the properties of the corresponding non-linear iterations, with emphasis on the geometrical constructions that can be used to classify the various solutions (for instance with or without reed beating) as well as on the periodicity windows that occur within the chaotic region. In particular, we find a regime where period tripling occurs and examine the conditions for intermittency. We also show that, while the direct observation of the iteration function does not reveal much on the oscillation regime of the instrument, the graph of the high order iterates directly gives visible information on the oscillation regime (characterization of the number of period doubligs, chaotic behaviour, etc.)

Stable Coexistence of an Invasive Plant and Biocontrol Agent: A Parameterized Coupled Plant-Herbivore Model

1. Coupled plant-herbivore models, allowing feedback from plant to herbivore populations and vice versa, enable us to predict the impact of biocontrol agents on their target weed populations; however, they are rarely used in biocontrol studies. We describe the population biology of the invasive plant Echium plantagineum and the weevil Mogulones larvatus, a biocontrol agent, in Australia. In order to understand the dynamics of this plant-herbivore system, a series of coupled models of increasing complexity was developed. 2. A simple model was extended to include a seed bank, density-dependent plant fecundity, competition between weevil larvae and plant tolerance of herbivory, where below a threshold plants could compensate for larval feeding. Parameters and functional forms were estimated from experimental and field data. 3. The plant model, in the absence of the weevil, exhibited stable dynamics and provided a good quantitative description of field densities before the weevil was introduced. 4. In the coupled plant-herbivore model, density dependence in both plant fecundity and weevil larval competition stabilized the dynamics. Without larval competition the model was unstable, and plant tolerance of herbivory exacerbated this instability. This was a result of a time delay in plant response to herbivore densities. 5. Synthesis and applications. The coupled plant-herbivore model allowed us to predict whether stable coexistence of target plant and biocontrol agents was achievable at an acceptable level. We found this to be the case for the Echium-Mogulones system and believe that similar models would be of use when assessing new agents in this and other invasive plant biocontrol systems. Density dependence in new biocontrol agents should be assessed in order to determine whether it is likely to result in the aims of classical biocontrol: low, stable and sustainable populations of plant and herbivore. Further work should be done to characterize the strength of density dependence according to the niche occupied by the biocontrol agent, for example the strength and functional form of density dependence in stem borers may be quite different to that of defoliators

Topology and correlations in structured scale-free networks

We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small world properties in the whole parameters range. We discuss the physical properties of these networks in the light of the present detailed analysis.Comment: 10 pages, 9 figure

Iron dextran in the treatment of iron-deficiency anaemia of pregnancy - Haematological response and incidence of side-effects

Sixty pregnant patients with a haemoglobin (Hb) < 8 g/dl arid proven iron-deficiency anaemia were randomly allocated to two treatment groups. Group A received the usual recommended dose of iron dextran (Imferon; Fisons) and group 8 received two-thirds of the recommended dose. A further 30 patients received oral iron (group C). There was no difference in Hb value between the three groups 4 weeks after treatment or 3 months after delivery. At 6 months after delivery, a higher mean Hb value was found in the patients in group A than those in groups 8 and C. Significantly higher serum ferritin levels were found in group A and this difference was still present 6 months postnatally. There was no significant difference in the incidence of delayed reactions between the two groups who received iron dextran