7 research outputs found
Reactive dynamics of inertial particles in nonhyperbolic chaotic flows
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open,
nonhyperbolic chaotic flows are important for many applications in biological,
chemical, and environmental sciences. We present a scaling theory for the
singular enhancement of the production caused by the universal, underlying
fractal patterns. The key dynamical invariant quantities are the effective
fractal dimension and effective escape rate, which are primarily determined by
the hyperbolic components of the underlying dynamical invariant sets. The
theory is general as it includes all previously studied hyperbolic reactive
dynamics as a special case. We introduce a class of dissipative embedding maps
for numerical verification.Comment: Revtex, 5 pages, 2 gif figure
Coevolution of Glauber-like Ising dynamics on typical networks
We consider coevolution of site status and link structures from two different
initial networks: a one dimensional Ising chain and a scale free network. The
dynamics is governed by a preassigned stability parameter , and a rewiring
factor , that determines whether the Ising spin at the chosen site flips
or whether the node gets rewired to another node in the system. This dynamics
has also been studied with Ising spins distributed randomly among nodes which
lie on a network with preferential attachment. We have observed the steady
state average stability and magnetisation for both kinds of systems to have an
idea about the effect of initial network topology. Although the average
stability shows almost similar behaviour, the magnetisation depends on the
initial condition we start from. Apart from the local dynamics, the global
effect on the dynamics has also been studied. These parameters show interesting
variations for different values of and , which helps in determining
the steady-state condition for a given substrate.Comment: 8 pages, 10 figure
Opinion dynamics: models, extensions and external effects
Recently, social phenomena have received a lot of attention not only from
social scientists, but also from physicists, mathematicians and computer
scientists, in the emerging interdisciplinary field of complex system science.
Opinion dynamics is one of the processes studied, since opinions are the
drivers of human behaviour, and play a crucial role in many global challenges
that our complex world and societies are facing: global financial crises,
global pandemics, growth of cities, urbanisation and migration patterns, and
last but not least important, climate change and environmental sustainability
and protection. Opinion formation is a complex process affected by the
interplay of different elements, including the individual predisposition, the
influence of positive and negative peer interaction (social networks playing a
crucial role in this respect), the information each individual is exposed to,
and many others. Several models inspired from those in use in physics have been
developed to encompass many of these elements, and to allow for the
identification of the mechanisms involved in the opinion formation process and
the understanding of their role, with the practical aim of simulating opinion
formation and spreading under various conditions. These modelling schemes range
from binary simple models such as the voter model, to multi-dimensional
continuous approaches. Here, we provide a review of recent methods, focusing on
models employing both peer interaction and external information, and
emphasising the role that less studied mechanisms, such as disagreement, has in
driving the opinion dynamics. [...]Comment: 42 pages, 6 figure
Commitment versus persuasion in the three-party constrained voter model
In the framework of the three-party constrained voter model, where voters of
two radical parties (A and B) interact with "centrists" (C and Cz), we study
the competition between a persuasive majority and a committed minority. In this
model, A's and B's are incompatible voters that can convince centrists or be
swayed by them. Here, radical voters are more persuasive than centrists, whose
sub-population consists of susceptible agents C and a fraction zeta of centrist
zealots Cz. Whereas C's may adopt the opinions A and B with respective rates
1+delta_A and 1+delta_B (with delta_A>=delta_B>0), Cz's are committed
individuals that always remain centrists. Furthermore, A and B voters can
become (susceptible) centrists C with a rate 1. The resulting competition
between commitment and persuasion is studied in the mean field limit and for a
finite population on a complete graph. At mean field level, there is a
continuous transition from a coexistence phase when
zeta=
Delta_c. In a finite population of size N, demographic fluctuations lead to
centrism consensus and the dynamics is characterized by the mean consensus time
tau. Because of the competition between commitment and persuasion, here
consensus is reached much slower (zeta=Delta_c) than
in the absence of zealots (when tau\simN). In fact, when zeta<Delta_c and there
is an initial minority of centrists, the mean consensus time asymptotically
grows as tau\simN^{-1/2} e^{N gamma}, where gamma is determined. The dynamics
is thus characterized by a metastable state where the most persuasive voters
and centrists coexist when delta_A>delta_B, whereas all species coexist when
delta_A=delta_B. When zeta>=Delta_c and the initial density of centrists is
low, one finds tau\simln N (when N>>1). Our analytical findings are
corroborated by stochastic simulations.Comment: 25 pages, 6 figures. Final version for the Journal of Statistical
Physics (special issue on the "applications of statistical mechanics to
social phenomena"
DISTRIBUTION AND SYNAPTIC ORGANIZATION OF SEROTONINERGIC AND NORADRENERGIC AXONS IN THE LATERAL GENICULATE-NUCLEUS OF THE RAT
Contact processes describe the transmission of distinct properties of nodes
via the links of a network. They provide a simple framework for many phenomena,
such as epidemic spreading and opinion formation. Combining contact processes
with rules for topological evolution yields an adaptive network in which the
states of the nodes can interact dynamically with the topological degrees of
freedom. By moment-closure approximation it is possible to derive
low-dimensional systems of ordinary differential equations that describe the
dynamics of the adaptive network on a coarse-grained level. In this chapter we
discuss the approximation technique itself as well as its applications to
adaptive networks. Thus, it can serve both as a tutorial as well as a review of
recent results.Comment: 18 pages, 5 figure
Cyclic dominance in adaptive networks
The Rock-Paper-Scissors (RPS) game is a paradigmatic model for cyclic dominance in
biological systems. Here we consider this game in the social context of competition
between opinions in a networked society. In our model, every agent has an opinion which is
drawn from the three choices: rock, paper or scissors. In every timestep a link is
selected randomly and the game is played between the nodes connected by the link. The
loser either adopts the opinion of the winner or rewires the link. These rules define an
adaptive network on which the agents’ opinions coevolve with the network topology of
social contacts. We show analytically and numerically that nonequilibrium phase
transitions occur as a function of the rewiring strength. The transitions separate four
distinct phases which differ in the observed dynamics of opinions and topology. In
particular, there is one phase where the population settles to an arbitrary consensus
opinion. We present a detailed analysis of the corresponding transitions revealing an
apparently paradoxical behavior. The system approaches consensus states where they are
unstable, whereas other dynamics prevail when the consensus states are stable