2,828 research outputs found
On competitive discrete systems in the plane. I. Invariant Manifolds
Let be a competitive map on a rectangular region . The main results of this paper give conditions which guarantee
the existence of an invariant curve , which is the graph of a continuous
increasing function, emanating from a fixed point . We show that
is a subset of the basin of attraction of and that the set consisting
of the endpoints of the curve in the interior of is forward invariant.
The main results can be used to give an accurate picture of the basins of
attraction for many competitive maps.
We then apply the main results of this paper along with other techniques to
determine a near complete picture of the qualitative behavior for the following
two rational systems in the plane.
with
and arbitrary nonnegative initial conditions so
that the denominator is never zero.
with
and arbitrary nonnegative initial conditions.Comment: arXiv admin note: text overlap with arXiv:0905.1772 by other author
Quasi-cycles in a spatial predator-prey model
We show that spatial models of simple predator-prey interactions predict that
predator and prey numbers oscillate in time and space. These oscillations are
not seen in the deterministic versions of the models, but are due to stochastic
fluctuations about the time-independent solutions of the deterministic
equations which are amplified due to the existence of a resonance. We calculate
the power spectra of the fluctuations analytically and show that they agree
well with results obtained from stochastic simulations. This work extends the
analysis of these quasi-cycles from that previously developed for well-mixed
systems to spatial systems, and shows that the ideas and methods used for
non-spatial models naturally generalize to the spatial case.Comment: 18 pages, 4 figure
The Shared Reward Dilemma
One of the most direct human mechanisms of promoting cooperation is rewarding
it. We study the effect of sharing a reward among cooperators in the most
stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically,
for a group of players that collect payoffs by playing a pairwise Prisoner's
Dilemma game with their partners, we consider an external entity that
distributes a fixed reward equally among all cooperators. Thus, individuals
confront a new dilemma: on the one hand, they may be inclined to choose the
shared reward despite the possibility of being exploited by defectors; on the
other hand, if too many players do that, cooperators will obtain a poor reward
and defectors will outperform them. By appropriately tuning the amount to be
shared a vast variety of scenarios arises, including traditional ones in the
study of cooperation as well as more complex situations where unexpected
behavior can occur. We provide a complete classification of the equilibria of
the -player game as well as of its evolutionary dynamics.Comment: Major rewriting, new appendix, new figure
Rewarding cooperation in social dilemmas
One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared we can cast a vast variety of scenarios, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a general class of public good games where competition among individuals with the same strategy exists.
When Geopolitics becomes Moral Panic: El Mercurio and the use of international news as propaganda against Salvador Allende’s Chile (1970–1973)
This article analyses how geopolitics was used to create moral panic during Salvador Allende’s government in Chile (1970–1973) and examines the type of recursive devices—such as geopolitical strategic narratives—that were employed by El Mercurio to advance specific discourses that intended to undermine the legitimacy of Allende while mobilising the public agenda towards the political right. Our thesis is that this was done by selective and framed use of international news in ways that somehow created moral panics by bringing geopolitics into the realm of the general public. In so doing, El Mercurio invisibilised important elements and effects of US Foreign Policy while highlighting similar elements and effects of the Soviet Foreign Policy. Our thesis is that in doing so, Allende’s government became associated with the ‘Red Scare’ and subsequently associated with the communist threat. This theme, we argue, remains relevant in times in which there continues to be a prevalent strategic narrative of enemies and foes in international news that continues to be used to create fear and mobilise public opinion towards the right of the political spectrum
Gravitating sphalerons and sphaleron black holes in asymptotically anti-de Sitter spacetime
Numerical arguments are presented for the existence of spherically symmetric
regular and black hole solutions of the EYMH equations with a negative
cosmological constant. These solutions approach asymptotically the anti-de
Sitter spacetime. The main properties of the solutions and the differences with
respect to the asymptotically flat case are discussed. The instability of the
gravitating sphaleron solutions is also proven.Comment: 30 pages, LaTeX, 8 Encapsulated PostScript figure
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