1,792 research outputs found
Discretized best-response dynamics for the rock-paper-scissors game
Discretizing a differential equation may change the qualitative behaviour drastically, even if the stepsize is small. We illustrate this by looking at the discretization of a piecewise continuous differential equation that models a population of agents playing the Rock-Paper-Scissors game. The globally asymptotically stable equilibrium of the differential equation turns, after discretization, into a repeller surrounded by an annulus shaped attracting region. In this region, more and more periodic orbits emerge as the discretization step approaches zero
Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations
A replicator equation with mutation processes is numerically studied.
Without any mutations, two characteristics of the replicator dynamics are
known: an exponential divergence of the dominance period, and hierarchical
orderings of the attractors. A mutation introduces some new aspects: the
emergence of structurally stable attractors, and chaotic itinerant behavior. In
addition, it is reported that a neutral attractor can exist in the mutataion
rate -> +0 region.Comment: 4 pages, 9 figure
Resonance bifurcations from robust homoclinic cycles
We present two calculations for a class of robust homoclinic cycles with
symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic
stability given by Krupa and Melbourne are not optimal.
Firstly, we compute optimal conditions for asymptotic stability using
transition matrix techniques which make explicit use of the geometry of the
group action.
Secondly, through an explicit computation of the global parts of the Poincare
map near the cycle we show that, generically, the resonance bifurcations from
the cycles are supercritical: a unique branch of asymptotically stable period
orbits emerges from the resonance bifurcation and exists for coefficient values
where the cycle has lost stability. This calculation is the first to explicitly
compute the criticality of a resonance bifurcation, and answers a conjecture of
Field and Swift in a particular limiting case. Moreover, we are able to obtain
an asymptotically-correct analytic expression for the period of the bifurcating
orbit, with no adjustable parameters, which has not proved possible previously.
We show that the asymptotic analysis compares very favourably with numerical
results.Comment: 24 pages, 3 figures, submitted to Nonlinearit
Random replicators with high-order interactions
We use tools of the equilibrium statistical mechanics of disordered systems
to study analytically the statistical properties of an ecosystem composed of N
species interacting via random, Gaussian interactions of order p >= 2, and
deterministic self-interactions u <= 0. We show that for nonzero u the effect
of increasing the order of the interactions is to make the system more
cooperative, in the sense that the fraction of extinct species is greatly
reduced. Furthermore, we find that for p > 2 there is a threshold value which
gives a lower bound to the concentration of the surviving species, preventing
then the existence of rare species and, consequently, increasing the robustness
of the ecosystem to external perturbations.Comment: 7 pages, 4 Postscript figure
Replica Symmetry Breaking in the Random Replicant Model
We study the statistical mechanics of a model describing the coevolution of
species interacting in a random way. We find that at high competition replica
symmetry is broken. We solve the model in the approximation of one step replica
symmetry breaking and we compare our findings with accurate numerical
simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request,
submitted to Journal of Physics A: Mathematical and Genera
PNP PIN bipolar phototransistors for high-speed applications built in a 180nm CMOS process
AbstractThis work reports on three speed optimized pnp bipolar phototransistors build in a standard 180nm CMOS process using a special starting wafer. The starting wafer consists of a low doped p epitaxial layer on top of the p substrate. This low doped p epitaxial layer leads to a thick space-charge region between base and collector and thus to a high −3dB bandwidth at low collector–emitter voltages. For a further increase of the bandwidth the presented phototransistors were designed with small emitter areas resulting in a small base-emitter capacitance. The three presented phototransistors were implemented in sizes of 40×40μm2 and 100×100μm2. Optical DC and AC measurements at 410nm, 675nm and 850nm were done for phototransistor characterization. Due to the speed optimized design and the layer structure of the phototransistors, bandwidths up to 76.9MHz and dynamic responsivities up to 2.89A/W were achieved. Furthermore simulations of the electric field strength and space-charge regions were done
Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities
The rock-paper-scissor game -- which is characterized by three strategies
R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and
R excludes S -- serves as a simple prototype for studying more complex
non-transitive systems. For well-mixed systems where interactions result in
fitness reductions of the losers exceeding fitness gains of the winners,
classical theory predicts that two strategies go extinct. The effects of
spatial heterogeneity and dispersal rates on this outcome are analyzed using a
general framework for evolutionary games in patchy landscapes. The analysis
reveals that coexistence is determined by the rates at which dominant
strategies invade a landscape occupied by the subordinate strategy (e.g. rock
invades a landscape occupied by scissors) and the rates at which subordinate
strategies get excluded in a landscape occupied by the dominant strategy (e.g.
scissor gets excluded in a landscape occupied by rock). These invasion and
exclusion rates correspond to eigenvalues of the linearized dynamics near
single strategy equilibria. Coexistence occurs when the product of the invasion
rates exceeds the product of the exclusion rates. Provided there is sufficient
spatial variation in payoffs, the analysis identifies a critical dispersal rate
required for regional persistence. For dispersal rates below , the
product of the invasion rates exceed the product of the exclusion rates and the
rock-paper-scissor metacommunities persist regionally despite being extinction
prone locally. For dispersal rates above , the product of the exclusion
rates exceed the product of the invasion rates and the strategies are
extinction prone. These results highlight the delicate interplay between
spatial heterogeneity and dispersal in mediating long-term outcomes for
evolutionary games.Comment: 31pages, 5 figure
Random Topologies and the emergence of cooperation: the role of short-cuts
We study in detail the role of short-cuts in promoting the emergence of
cooperation in a network of agents playing the Prisoner's Dilemma Game (PDG).
We introduce a model whose topology interpolates between the one-dimensional
euclidean lattice (a ring) and the complete graph by changing the value of one
parameter (the probability p to add a link between two nodes not already
connected in the euclidean configuration). We show that there is a region of
values of p in which cooperation is largely enhanced, whilst for smaller values
of p only a few cooperators are present in the final state, and for p
\rightarrow 1- cooperation is totally suppressed. We present analytical
arguments that provide a very plausible interpretation of the simulation
results, thus unveiling the mechanism by which short-cuts contribute to promote
(or suppress) cooperation
Robustness and epistasis in mutation-selection models
We investigate the fitness advantage associated with the robustness of a
phenotype against deleterious mutations using deterministic mutation-selection
models of quasispecies type equipped with a mesa shaped fitness landscape. We
obtain analytic results for the robustness effect which become exact in the
limit of infinite sequence length. Thereby, we are able to clarify a seeming
contradiction between recent rigorous work and an earlier heuristic treatment
based on a mapping to a Schr\"odinger equation. We exploit the quantum
mechanical analogy to calculate a correction term for finite sequence lengths
and verify our analytic results by numerical studies. In addition, we
investigate the occurrence of an error threshold for a general class of
epistatic landscape and show that diminishing epistasis is a necessary but not
sufficient condition for error threshold behavior.Comment: 20 pages, 14 figure
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