18 research outputs found
A New Type of Irregular Motion in a Class of Game Dynamics Systems
A new type of asymptotic behavior in a game dynamics system is discovered.
The system exhibits behavior which combines chaotic motion and attraction to
heteroclinic cycles; the trajectory visits several unstable stationary states
repeatedly with an irregular order, and the typical length of the stay near the
steady states grows exponentially with the number of visits. The dynamics
underlying this irregular motion is analyzed by introducing a dynamically
rescaled time variable, and its relation to the low-dimensional chaotic
dynamics is thus uncovered. The relation of this irregular motion with a
strange type of instability of heteroclinic cycles is also examined.Comment: 7 pages (Revtex) + 4 figures (postscript
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
Noiseless Collective Motion out of Noisy Chaos
We consider the effect of microscopic external noise on the collective motion
of a globally coupled map in fully desynchronized states. Without the external
noise a macroscopic variable shows high-dimensional chaos distinguishable from
random motion. With the increase of external noise intensity, the collective
motion is successively simplified. The number of effective degrees of freedom
in the collective motion is found to decrease as with the
external noise variance . It is shown how the microscopic noise can
suppress the number of degrees of freedom at a macroscopic level.Comment: 9 pages RevTex file and 4 postscript figure
Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems
Starting with a group of reinforcement-learning agents we derive coupled
replicator equations that describe the dynamics of collective learning in
multiagent systems. We show that, although agents model their environment in a
self-interested way without sharing knowledge, a game dynamics emerges
naturally through environment-mediated interactions. An application to
rock-scissors-paper game interactions shows that the collective learning
dynamics exhibits a diversity of competitive and cooperative behaviors. These
include quasiperiodicity, stable limit cycles, intermittency, and deterministic
chaos--behaviors that should be expected in heterogeneous multiagent systems
described by the general replicator equations we derive.Comment: 4 pages, 3 figures,
http://www.santafe.edu/projects/CompMech/papers/credlmas.html; updated
references, corrected typos, changed conten
Collective motions in globally coupled tent maps with stochastic updating
We study a generalization of globally coupled maps, where the elements are
updated with probability . When is below a threshold , the
collective motion vanishes and the system is the stationary state in the large
size limit. We present the linear stability analysis.Comment: 6 pages including 5 figure
Infinities of stable periodic orbits in systems of coupled oscillators
We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor