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Caravelli F.,Invenia Labs | Caravelli F.,London Institute of Mathematical science | Caravelli F.,University College London | Staniczenko P.P.A.,University of Maryland University College | Staniczenko P.P.A.,National Socio Environmental Synthesis Center

Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse effects. In ecology, the Jacobian matrix evaluated at an equilibrium point is known as the community matrix, which describes the population dynamics of interacting species. A system's asymptotic short- and long-term behaviour can be determined from eigenvalues derived from the community matrix. Here we use results from the theory of pseudospectra to describe intermediate, transient dynamics. We first recover the established result that the transition from stable to unstable dynamics includes a region of 'transient instability', where the effect of a small perturbation to species' abundances-to the population vector-is amplified before ultimately decaying. Then we show that the shift from stability to transient instability can be affected by uncertainty in, or small changes to, entries in the community matrix, and determine lower and upper bounds to the maximum amplitude of perturbations to the population vector. Of five different types of community matrix, we find that amplification is least severe when predator-prey interactions dominate. This analysis is relevant to other systems whose dynamics can be expressed in terms of the Jacobian matrix. © 2016 Caravelli, Staniczenko. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Source

Scala A.,University of Rome La Sapienza | Scala A.,London Institute of Mathematical science
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

The blossoming of interest in colloids and nanoparticles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration time step. This is not the case for hard-body systems, where there is no clear-cut distinction between the correlation time of the noise and the time scale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two algorithms for the simulation of the Langevin dynamics of hard spheres. © 2012 American Physical Society. Source

Banchi L.,University College London | Caravelli F.,Invenia Labs | Caravelli F.,London Institute of Mathematical science
Classical and Quantum Gravity

In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker Universe with a periodic scale factor, in which the Universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this Universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrary to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs as generically non-zero. The Berry phase is then evaluated numerically in the case of the effective loop quantum cosmology closed Universe. We observe that Berry's phase is non-zero, but that in the quantum regime the particle content is non-negligible. © 2016 IOP Publishing Ltd. Source

Zhou D.,Boston University | Stanley H.E.,Boston University | D'Agostino G.,ENEA | Scala A.,University of Rome La Sapienza | Scala A.,London Institute of Mathematical science
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and, hence, systemwide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e., the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture and, thus, enhance the level of protection of critical infrastructures. © 2012 American Physical Society. Source

D'Agostino G.,ENEA | Scala A.,University of Rome La Sapienza | Scala A.,London Institute of Mathematical science | Zlatic V.,Ruder Boskovic Institute | And 2 more authors.

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk. © 2012 Europhysics Letters Association. Source

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