Noise-induced breakdown of coherent collective motion in swarms

We consider swarms formed by populations of self-propelled particles with attractive long-range interactions. These swarms represent multistable dynamical systems and can be found either in coherent traveling states or in an incoherent oscillatory state where translational motion of the entire swarm is absent. Under increasing the noise intensity, the coherent traveling state of the swarms is destroyed and an abrupt transition to the oscillatory state takes place.Comment: 6 pages, 5 figures; to appear in Phys. Rev.

On the genealogy of a population of biparental individuals

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number Gc ~ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gc generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.Comment: 14 pages, 7 figures, to appear in the Journal of Theoretical Biolog

Wave fronts in bistable reactions with anomalous Lévy-flight diffusion

Shape-preserving traveling solutions of an equation describing the interplay of bistable reaction processes and Lévy-flight anomalous diffusion are obtained and analyzed. The velocity of these wave fronts is determined as a function of the reaction parameters and the anomalous-diffusion exponent, and their shape is characterized in terms of simple quantities

Dynamics of globally coupled bistable elements

The macroscopic dynamics of a large set of globally coupled, identical, noiseless, bistable elements is analytically and numerically studied. Depending on the value of the coupling constant and on the initial condition, all the elements can either evolve towards the same individual state or become divided into two groups, which approach two different states. It is shown that at a critical value of the coupling constant the system undergoes a transition from bistable evolution, where the two behaviors described above can occur, to coherent evolution, where the convergence towards the same individual state is the only possible behavior. Connections of this system with the real Ginzburg-Landau equation and with the sociological problem of opinion formation are discussed

Persistence in Lévy-flight anomalous diffusion

The evolution of the number of persistent sites in a field governed by Lévy-flight anomalous diffusion is characterized. It is shown that, as in the case of ordinary diffusion, the number of persistent sites exhibits a long-time power-law decay. For the case of white-noise initial conditions, the exponent in this power-law decay can be numerically found from an algebraic equation as a function of the Lévy exponent γ. As expected, the decay is faster as the transport mechanism becomes more efficient, i.e., as γ decreases. Numerical simulations that validate the analytical results are also presented

Disturbing synchronization: Propagation of perturbations in networks of coupled oscillators

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the interaction network underlying the ensemble. The overall response of the system is resonant, exhibiting a maximum when the perturbation frequency coincides with the natural frequency of the phase oscillators. The individual response, on the other hand, can strongly depend on the distance to the place where the perturbation is applied. For small distances on a random network, the system behaves as a linear dissipative medium: the perturbation propagates at constant speed, while its amplitude decreases exponentially with the distance. For larger distances, the response saturates to an almost constant level. These different regimes can be analytically explained in terms of the length distribution of the paths that propagate the perturbation signal. We study the extension of these results to other interaction patterns, and show that essentially the same phenomena are observed in networks of chaotic oscillators.Comment: To appear in Eur. Phys. J.

Role of Intermittency in Urban Development: A Model of Large-Scale City Formation

A stochastic model that incorporates the essential mechanisms supposed to govern city formation is numerically analyzed. The model generates intermittent spatiotemporal structures and predicts a power-law population distribution whose exponent is in excellent agreement with the universal exponent observed in real human demography. Preliminary results of cluster analysis of the model also coincide with actual data. We thus suggest that urban development at large scales could be driven by intermittency processes

Mutual synchronization in ensembles of globally coupled neural networks

The collective dynamics in globally coupled ensembles of identical neural networks with random asymmetric synaptic connections is investigated. We find that this system shows a spontaneous synchronization transition, i.e., networks with synchronous activity patterns appear in the ensemble when the coupling intensity exceeds a threshold. Under further increase of the coupling intensity, the entire ensemble breaks down into a number of coherent clusters, until complete mutual synchronization is eventually established