Journal ArticleDOI
Hopf bifurcation for functional differential equations of mixed type
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In this paper, the authors prove Hopf bifurcation and center manifold theorems for functional differential equations of mixed type and apply them to the dynamic behavior of a competitive economy.Abstract:
We prove Hopf bifurcation and center manifold theorems for functional differential equations of mixed type. An application to the dynamic behavior of a competitive economy (business cycle) is provided.read more
Citations
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Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Journal ArticleDOI
The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems
TL;DR: In this article, the existence of traveling wave solutions for a class of spatially discrete systems, namely, lattice differential equations, was proved for lattice lattice systems, and the global structure of the set of all traveling wave solution is shown to be a smooth manifold where c ≥ 0.
Journal ArticleDOI
The Fredholm Alternative for Functional Differential Equations of Mixed Type
TL;DR: In this paper, a Fredholm alternative theorem for a class of asymptotically hyperbolic linear differential difference equations of mixed type was proved, which can arise from equations which describe traveling waves in a spatial lattice.
Journal ArticleDOI
Vintage capital, investment, and growth☆
Jess Benhabib,Aldo Rustichini +1 more
TL;DR: In this paper, the authors study the dynamics of growth and investment in a continuous time model with vintage capital, which is characterized by nonexponential rates of depreciation and technical change and can incorporate "gestation lags" as well as "learning by using".
Journal ArticleDOI
Traveling wave solutions for systems of ODEs on a two-dimensional spatial lattice
TL;DR: It is shown that a :R!R is continuous at each point where tan is irrational, and is discontinuousWhere tan is rational or innite, and it is explored the relation between the wave speed c, the angle, and the detuning parameter a of the nonlinearity.
References
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Book
Theory of Functional Differential Equations
TL;DR: In this paper, Liapunov functional for autonomous systems is used to define the saddle point property near equilibrium and periodic orbits for linear systems, which is a generalization of the notion of stable D operators.
Journal ArticleDOI
Time to build and aggregate fluctuations
TL;DR: In this article, a general equilibrium model is developed and fitted to U.S. quarterly data for the post-war period, with the assumption that more than one time period is required for the construction of new productive capital and the non-time-separable utility function that admits greater intertemporal substitution of leisure.
BookDOI
Singularities and groups in bifurcation theory
TL;DR: Singularities and groups in bifurcation theory as mentioned in this paper have been used to solve the problem of finding a group of singularities in a set of problems with multiple solutions.
Book
Differential-Difference Equations
Richard Bellman,Kenneth L. Cooke +1 more
TL;DR: In this paper, the authors introduce the study of differential difference equations and discuss some of the main features of the theory, and discuss the asymptotic behavior of solutions and the problem of stability.