32 research outputs found
Spurious memory in non-equilibrium stochastic models of imitative behavior
The origin of the long-range memory in the non-equilibrium systems is still
an open problem as the phenomenon can be reproduced using models based on
Markov processes. In these cases a notion of spurious memory is introduced. A
good example of Markov processes with spurious memory is stochastic process
driven by a non-linear stochastic differential equation (SDE). This example is
at odds with models built using fractional Brownian motion (fBm). We analyze
differences between these two cases seeking to establish possible empirical
tests of the origin of the observed long-range memory. We investigate
probability density functions (PDFs) of burst and inter-burst duration in
numerically obtained time series and compare with the results of fBm. Our
analysis confirms that the characteristic feature of the processes described by
a one-dimensional SDE is the power-law exponent of the burst or
inter-burst duration PDF. This property of stochastic processes might be used
to detect spurious memory in various non-equilibrium systems, where observed
macroscopic behavior can be derived from the imitative interactions of agents.Comment: 11 pages, 5 figure
Control of the socio-economic systems using herding interactions
Collective behavior of the complex socio-economic systems is heavily
influenced by the herding, group, behavior of individuals. The importance of
the herding behavior may enable the control of the collective behavior of the
individuals. In this contribution we consider a simple agent-based herding
model modified to include agents with controlled state. We show that in certain
case even the smallest fixed number of the controlled agents might be enough to
control the behavior of a very large system.Comment: 8 pages, 3 figure
Fluctuation analysis of the three agent groups herding model
We derive a system of stochastic differential equations simulating the
dynamics of the three agent groups with herding interaction. Proposed approach
can be valuable in the modeling of the complex socio-economic systems with
similar composition of the agents. We demonstrate how the sophisticated
statistical features of the absolute return in the financial markets can be
reproduced by extending the herding interaction of the agents and introducing
the third agent state. As well we consider possible extension of proposed
herding model introducing additional exogenous noise. Such consistent
microscopic and macroscopic model precisely reproduces empirical power law
statistics of the return in the financial markets.Comment: 9 pages, 2 figure
Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model
Systems with long-range interactions often exhibit power-law distributions
and can by described by the non-extensive statistical mechanics framework
proposed by Tsallis. In this contribution we consider a simple model
reproducing continuous transition from the extensive to the non-extensive
statistics. The considered model is composed of agents interacting among
themselves on a certain network topology. To generate the underlying network we
propose a new network formation algorithm, in which the mean degree scales
sub-linearly with a number of nodes in the network (the scaling depends on a
single parameter). By changing this parameter we are able to continuously
transition from short-range to long-range interactions in the agent-based
model.Comment: 12 pages, 6 figure