22,598 research outputs found
Multi-agent decision-making dynamics inspired by honeybees
When choosing between candidate nest sites, a honeybee swarm reliably chooses
the most valuable site and even when faced with the choice between near-equal
value sites, it makes highly efficient decisions. Value-sensitive
decision-making is enabled by a distributed social effort among the honeybees,
and it leads to decision-making dynamics of the swarm that are remarkably
robust to perturbation and adaptive to change. To explore and generalize these
features to other networks, we design distributed multi-agent network dynamics
that exhibit a pitchfork bifurcation, ubiquitous in biological models of
decision-making. Using tools of nonlinear dynamics we show how the designed
agent-based dynamics recover the high performing value-sensitive
decision-making of the honeybees and rigorously connect investigation of
mechanisms of animal group decision-making to systematic, bio-inspired control
of multi-agent network systems. We further present a distributed adaptive
bifurcation control law and prove how it enhances the network decision-making
performance beyond that observed in swarms
Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in
We investigate coarse equilibrium states of a fine-scale, stochastic
agent-based model of consumer lock-in in a duopolistic market. In the model,
agents decide on their next purchase based on a combination of their personal
preference and their neighbours' opinions. For agents with independent
identically-distributed parameters and all-to-all coupling, we derive an
analytic approximate coarse evolution-map for the expected average purchase. We
then study the emergence of coarse fronts when spatial segregation is present
in the relative perceived quality of products. We develop a novel Newton-Krylov
method that is able to compute accurately and efficiently coarse fixed points
when the underlying fine-scale dynamics is stochastic. The main novelty of the
algorithm is in the elimination of the noise that is generated when estimating
Jacobian-vector products using time-integration of perturbed initial
conditions. We present numerical results that demonstrate the convergence
properties of the numerical method, and use the method to show that macroscopic
fronts in this model destabilise at a coarse symmetry-breaking bifurcation.Comment: This version of the manuscript was accepted for publication on SIAD
Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
We analyze a large system of globally coupled phase oscillators whose natural
frequencies are bimodally distributed. The dynamics of this system has been the
subject of long-standing interest. In 1984 Kuramoto proposed several
conjectures about its behavior; ten years later, Crawford obtained the first
analytical results by means of a local center manifold calculation.
Nevertheless, many questions have remained open, especially about the
possibility of global bifurcations. Here we derive the system's complete
stability diagram for the special case where the bimodal distribution consists
of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott
and Antonsen, we show that in this case the infinite-dimensional problem
reduces exactly to a flow in four dimensions. Depending on the parameters and
initial conditions, the long-term dynamics evolves to one of three states:
incoherence, where all the oscillators are desynchronized; partial synchrony,
where a macroscopic group of phase-locked oscillators coexists with a sea of
desynchronized ones; and a standing wave state, where two counter-rotating
groups of phase-locked oscillators emerge. Analytical results are presented for
the bifurcation boundaries between these states. Similar results are also
obtained for the case in which the bimodal distribution is given by the sum of
two Gaussians.Comment: 28 pages, 7 figures; submitted to Phys. Rev. E Added comment
Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling
Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region.
We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell–cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region.
However, real tissues are heterogeneous with spatial changes in cell–cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell–cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient
The case of the trapped singularities
A case study in bifurcation and stability analysis is presented, in which
reduced dynamical system modelling yields substantial new global and predictive
information about the behaviour of a complex system. The first smooth pathway,
free of pathological and persistent degenerate singularities, is surveyed
through the parameter space of a nonlinear dynamical model for a
gradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas.
Along the route various obstacles and features are identified and treated
appropriately. An organizing centre of low codimension is shown to be robust,
several trapped singularities are found and released, and domains of
hysteresis, threefold stable equilibria, and limit cycles are mapped.
Characterization of this rich dynamical landscape achieves unification of
previous disparate models for plasma confinement transitions, supplies valuable
intelligence on the big issue of shear flow suppression of turbulence, and
suggests targeted experimental design, control and optimization strategies.Comment: 21 pages, 12 figures, 34 postscript figure file
- …