arXiv subjects

Damian H. Zanette

Publications and source records attributed to Damian H. Zanette.

49 records · Page 3Linked to original sources

arXiv2001

Criticality of rumor propagation on small-world networks

We show that a simple model for the propagation of a rumor on a small-world network exhibits critical behavior at a finite randomness of the underlying graph. The transition occurs between a regime where the rumor "dies" in a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the whole population. Critical exponents are evaluated through finite-size scaling analysis, and the dependence of the critical randomness with the network connectivity is studied. The behavior of this system as a function of the network randomness bears noticeable similarities with an epidemiological model reported recently [M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)], in spite of substantial differences in the respective dynamical rules.

cond-mat.stat-mech↗

arXiv2001

Critical behavior of propagation on small-world networks

We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a regime where the rumor "dies" in a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the whole population. Critical exponents are evaluated, and the dependence of the critical randomness with the network connectivity is studied. The behavior of this system as a function of the small-network randomness bears noticeable similarities with an epidemiological model reported recently [M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)], in spite of substantial differences in the respective dynamical rules.

cond-mat.stat-mech↗

arXiv2001

Anticipated synchronization in coupled chaotic maps with delays

We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay $n_1$, and coupling acts with a delay $n_2$. Depending on the sign of the difference $n_1-n_2$, the slave map can synchronize to a future or a past state of the master system. The stability properties of the synchronized state are studied analytically, and we find that they are independent of the coupling delay $n_2$. These results are compared with numerical simulations of a delayed map that arises from discretization of the Ikeda delay-differential equation. We show that the critical value of the coupling strength above which synchronization is stable becomes independent of the delay $n_1$ for large delays.

nlin.CD↗

arXiv2000

Complex spatial organization in a simple model of resource allocation

A dynamical model for the distribution of resources between competing agents is studied. While global competition leads to the accumulation of all the resources by a single agent, local competition allows for a wider resource distribution. Multiplicative processes give rise to almost-ordered spatial structures, thourgh the enhancement of random fluctuations.

nlin.AO↗

arXiv2000

Synchronization of Kauffman networks

We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides an approximate description for the whole dynamics of the coupled networks. We show that these analytical predictions are in good agreement with numerical results for sufficiently large networks, and study finite-size effects in detail. Preliminary analytical and numerical results for partially disordered networks are also presented.

nlin.AO↗

arXiv2000

Synchronization learning of coupled chaotic maps

We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization. Numerical calculations reveal a sharp transition between regimes of unsuccessful and successful learning as the algorithm stiffness grows. In the regime of successful learning, an optimal value of the stiffness is found for which the learning time is minimal.

nlin.AO↗

arXiv2000

Vertical transmission of culture and the distribution of family names

A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted exponents are in good agreement with real data. The evolution of family-name distributions is discussed in the frame of vertical transmission of cultural features.

nlin.AO↗

arXiv2000

Structures and propagation in globally coupled systems with time delays

We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We show that one-dimensional arrays synchronize in an asymptotic state where all the oscillators have the same frequency, whereas their phases are distributed in spatial structures that -in the case of periodic boundaries- can propagate, much as in coupled systems with local interactions.

cond-mat.stat-mech↗

arXiv1999

Globally coupled bistable elements as a model of group decision making

A simple mathematical model is proposed to study the effect of the average trend of a population on the opinion of each individual, when a group decision has to be made by voting. It is shown that if such effect is strong enough a transition to coherent behavior occurs, in which the whole population converges to a single opinion. This transition has the character of a first-order critical phenomenon.

adap-org↗

arXiv1999

Statistical-thermodynamical foundations of anomalous diffusion

It is shown that Tsallis' generalized statistics provides a natural frame for the statistical-thermodynamical description of anomalous diffusion. Within this generalized theory, a maximum-entropy formalism makes it possible to derive a mathematical formulation for the mechanisms that underly Levy-like superdiffusion, and for solving the nonlinear Fokker-Planck equation.

cond-mat.stat-mech↗

arXiv1999

Stochastic multiplicative processes with reset events

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behaviour. In the boundary between them, the mean value of the relevant variable is time-independent, and the exponent of the stationary distribution equals -2. The addition of diffusion to the system modifies in a non-trivial way the profile of the stationary distribution. Numerical and analytical results are presented.

cond-mat↗

arXiv1999

Statistical properties of genealogical trees

We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution, we measure the distribution of ancestors appearing more than once in a given tree. After a transient time, the probability of repetition follows, up to a rescaling, a stationary distribution which we calculate both numerically and analytically. This distribution exhibits a universal shape with a non-trivial power law which can be understood by an exact, though simple, renormalization calculation. Some real data on human genealogy illustrate the problem, which is relevant to the study of the real degree of diversity in closed interbreeding communities.

cond-mat↗

arXiv1998

Globally coupled maps with asynchronous updating

We analyze a system of globally coupled logistic maps with asynchronous updating. We show that its dynamics differs considerably from that of the synchronous case. For growing values of the coupling intensity, an inverse bifurcation cascade replaces the structure of clusters and ordering in the phase diagram. We present numerical simulations and an analytical description based on an effective single-element dynamics affected by internal fluctuations. Both of them show how global coupling is able to suppress the complexity of the single-element evolution. We find that, in contrast to systems with synchronous update, internal fluctuations satisfy the law of large numbers.

chao-dyn↗