The Theory of Dynamical Systems ,and its Applications to Economics
الكلمات المفتاحية:
Adjustment economic processes، Stability of Equilibrium، Lyapunov function، Hopf bifurcation، Chaosالملخص
This paper is devoted to the theory of dynamical systems and its applications to Economics. First, the paper presents some adjustment economic processes, and studies the question of stability of equilibrium. Second, some economic models will be presented that exhibit bifurcation and chaotic phenomena.المراجع
Arrow K.J. and L .Hurwicz (1958), “On the Stability of the Competitive Equilibrium " Econometrica 26 , 522-552.
Bartle ,R.G and D.R. Sherbert (1992) ."Introduction to Real Analysis" 2 nd Edition New York Wiley
Beja, A and Goldman,M.B ( 1980) " On the Dynamic behavior of Prices in Disequilibrium " Journal of Finance ,XXXV (2) pp.235-248.
Birkhoff,G.D (1927) Dynamical Systems, AMS Publications : Providence.
Hofbauer ,J. and K. Sigmund (1988) ,"The Theory of Evolution and Dynamical Systems ", Cambridge : Cambridge University Press .
Debreu ,Gerard (1975)," The Rate of Convergence of the Core of an Economy ", Journal of Mathematical Economy,2 ,1-7
Scarf, H (1960), “Some Examples of Global Instability of the Competitive Equilibrium", International Economic Review, 1,157-172.
Brown, J. Donald and Shannon C. (1998) , " Uniqueness, Stability,and Comparative Statics in Rationalizable Walrasian markets"
George ,D (1981) " Equilibrium and Catastrophes in Economics " Scottish Journal of Political Economy ,28, pp. 43-61.
Gopalswany,K. and Aggarwala B.D (1980) , " Limit Cycles in Two Species Competition with Time Delays" Journal of the Australian mathematical Society, Series B- Applied Mathematics ,22, (2) ,pp-148-160.
Herings ,P J-J (1997) " A globally and universally stable price adjustment process" Journal of Mathematical Economics 27: 163-193.
Hermann J.D and P. J. Kahn (1999) " A continuity property for local price adjustment mechanisms " Journal of Mathematical Economics 31: 419-453
Joosten R. ,and D. Talman.( 1998) "A globally convergent price adjustment process for exchange economies "Journal of Mathematical Economies 29: 15-26
Kamiya K. (1990) " A globally stable price adjustment process ' Econometrica ,58 (6) pp. 1481-1485
Lorenz,H.W. (1989) "Non linear Dynamical Economics and Chaotic Motion" Springer Verlag Lecture Notes in Economics and mathematical systems, Vol. 334.
Mukherji ,A. (1995) ." A locally stable adjustment process " Econometrica 63 (2) ; 441-448
Smale ,S. (1976) " A convergent process of price adjustment and Global Newton methods" Journal of Mathematical Economics .3 : 107-120.
Szentkuti Zs . (1998) " periodic solutions in May-Leonard type population dynamic models" Alkalmazott matematikai Lapok ,19, 23-38.
Uzawa H, (1962) "Walras' Existence Theorem and Brower's fixed point Theorem" Economic Studies Quarterly , 8, 59-62.
Van der Laan ,G and A.J.J Talman (1987) : A convergent price adjustment process " Economic Letters ,23 pp: 119-123.
Varian ,H.R. (1979) "Catastrophe Theory and the Business Cycle " , Economic Inquiry,17 pp-14-28
Weintraub,E.R. (1983) . " On the Existence of Competitive Equilibrium" Journal of Economic Literature, XXI,1-39.
Zeeman ,M .L. (1993) " Hopf bifurcations in Lotka –Volterra systems " Dynamics and Stability of Systems,8, 189-217
Zeeman,E.C (1974) " On the Unstable Behavior of Stock Exchanges" Journal of Mathematical Economics, 1, pp. 39-49.
