Traveling waves in a mean field learning model
نویسندگان
چکیده
Lucas and Moll have proposed a system of forward-backward partial differential equations that model knowledge diffusion economic growth. It arises from microscopic learning for mean-field type interacting individual agents. In this paper, we prove existence traveling wave solutions to system. They correspond what is known in economics as balanced growth path solutions. We also study the dependence their propagation speed on various parameters
منابع مشابه
Construction of traveling clusters in the Hamiltonian mean-field model by nonequilibrium statistical mechanics and Bernstein-Greene-Kruskal waves.
Traveling clusters are ubiquitously observed in the Hamiltonian mean-field model for a wide class of initial states, which are not predicted to become spatially inhomogeneous states by nonequilibrium statistical mechanics and by nonlinear Landau damping. To predict such a cluster state from a given initial state, we combine nonequilibrium statistical mechanics and a construction method of Berns...
متن کاملMean-Field Learning: a Survey
In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the best reply map is not a contraction, Ishikawa-based learning is proposed. The a...
متن کاملA Geometric Construction of Traveling Waves in a Bioremediation Model
Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil column. Using geometric singular perturbation theory, we construct traveling waves (TW) corresponding to motion of a biologically active zone, in whic...
متن کاملTraveling Waves in a Convolution Model for Phase Transitions
The existence, uniqueness, stability and regularity properties of traveling wave solutions of a bistable nonlinear integrodifferential equation=20 are established, as well as their global asymptotic stability in the case of zero velocity continuous waves. =20 This equation is a direct analog of the more familiar=20 bistable nonlinear diffusion equation, and shares many of its properties. = It=2...
متن کاملExistence of Traveling Waves in a Neural Model
In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of travelling wave fronts for a differential-integral equation modeling a neural network. Since then a number of authors have extended the model by adding an additional equation for a “recovery variable”, thus allowing the possibility of travelling pulse type solutions. In a recent paper G. Faye gave perhaps the first rigorous...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2021
ISSN: ['0951-7715', '1361-6544']
DOI: https://doi.org/10.1088/1361-6544/abcc4d