Center for Economic Research, Department of Economics, University of Minnesota
The purpose of this paper is to analyze stability of a system of
piecewise continuous differential equations, and its application to disequilibrium
economic models. A unique solution in the sense of Filippov
for such a system is defined and claimed to exist. This problem frequently
appears in disequilibrium models, since the so-called " shortside"
rule assigns either demand or supply to the transaction amount which
is a state variable of an economic system. The concept of Filippov solution
makes it possible to analyze a dynamic evolution of such a model. This
paper demonstrates that (i) stability conditions for each piecewise system
of differential equations are neither necessary nor sufficient for the
overall stability with regime switching, except special cases such as a
system of linear differential equations in R2, with two regimes separated
by a linear boundary; (ii) several sufficient conditions for an overall
stability with many regimes are available, making use of a Lyapunov function
common to all regimes; (iii) stability theorems with regime switching are
useful for disequilibrium economic models with several regimes.
Honkapohja, S. and Ito, T., (1980), "Stability with Regime Switching", Discussion Paper No. 130, Center for Economic Research, Department of Economics, University of Minnesota.
Honkapohja, Seppo; Ito, Takatoshi.
Stability with Regime Switching.
Center for Economic Research, Department of Economics, University of Minnesota.
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