Complex dynamics in a simple model of interdependent open economies

Based on a simple two-market model, characterized by a demand link between competitive markets for goods, a system of coupled difference equations is used to represent the interdependent structure of a global economy. Relying on numerical and analytical approaches, Various dynamic properties of the proposed model are explored. Among others, a general specification of the regions of stability of the equilibrium and main periodic cycles, the transition to chaos through torus destruction, chaotic synchronization, and the coexistence of different types of attractors in parameter space are described. Typical bifurcation processes are illustrated.

[1]  A. Dixit,et al.  Monopolistic competition and optimum product diversity , 1977 .

[2]  Paul S. Armington.  A Theory of Demand for Products Distinguished by Place of Production (Une théorie de la demande de produits différenciés d'après leur origine) (Una teoría de la demanda de productos distinguiéndolos según el lugar de producción) , 1969 .

[3]  I. Kubin,et al.  Non-linearities and partial analysis , 1995 .

[4]  James A. Yorke,et al.  Dynamics: Numerical Explorations , 1994 .

[5]  I. Stewart,et al.  From attractor to chaotic saddle: a tale of transverse instability , 1996 .

[6]  R. Jones.  International trade: Essays in theory , 1979 .

[7]  Ragnar Torvik,et al.  Zimbabwean Trade Liberalisation: Ex Post Evaluation , 1998 .

[8]  C. Hommes,et al.  Partial equilibrium analysis in a noisy chaotic market , 1996 .

[9]  James A. Yorke,et al.  Analysis of a procedure for finding numerical trajectories close to chaotic saddle hyperbolic sets , 1991, Ergodic Theory and Dynamical Systems.

[10]  David G. Tarr,et al.  Economic Implications for Turkey of a Customs Union with the European Union , 1996 .

[11]  Ljupco Kocarev,et al.  General approach for chaotic synchronization with applications to communication. , 1995, Physical review letters.

[12]  Roy,et al.  Experimental synchronization of chaotic lasers. , 1994, Physical review letters.

[13]  Environmental and trade policies: some methodological lessons , 1996, Environment and Development Economics.

[14]  Floris Takens,et al.  Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors , 1993 .

[15]  Elhanan Helpman,et al.  Trade policy and market structure , 1990 .

[16]  P. Grassberger,et al.  Symmetry breaking bifurcation for coupled chaotic attractors , 1991 .

[17]  William A. Brock,et al.  A rational route to randomness , 1997 .

[18]  Parlitz,et al.  General approach for chaotic synchronization with applications to communication. , 1995, Physical Review Letters.

[19]  B. Ohlin,et al.  Interregional and International Trade. , 1936 .

[20]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[21]  Arkady Pikovsky,et al.  On the interaction of strange attractors , 1984 .

[22]  Christian Mira,et al.  Chaotic Dynamics in Two-Dimensional Noninvertible Maps , 1996 .

[23]  Yuri Maistrenko,et al.  An introduction to the synchronization of chaotic systems: coupled skew tent maps , 1997 .

[24]  N. Karunaratne.  Macroeconomic Insights on the Liberalized Trading Regime of Thailand , 2012 .

[25]  Can The World Trading System Accommodate More East Asian Style Exporters , 1997 .

[26]  N. Rulkov,et al.  Robustness of Synchronized Chaotic Oscillations , 1997 .

[27]  Kar-yiu Wong,et al.  International Trade in Goods and Factor Mobility , 1995 .

[28]  Louis M. Pecora,et al.  Fundamentals of synchronization in chaotic systems, concepts, and applications. , 1997, Chaos.

[29]  W. Thurston,et al.  On iterated maps of the interval , 1988 .

[30]  J. Milnor.  On the concept of attractor , 1985 .

[31]  R. Johns.  International Trade Theories and the Evolving International Economy , 1985 .

[32]  Unfolding of the riddling bifurcation , 1999 .

[33]  E. Ott,et al.  Blowout bifurcations: the occurrence of riddled basins and on-off intermittency , 1994 .

[34]  Tomasz Kapitaniak,et al.  Riddling bifurcations in coupled piecewise linear maps , 1999 .

[35]  Tomasz Kapitaniak,et al.  Loss of Chaos Synchronization through the Sequence of Bifurcations of Saddle Periodic Orbits , 1997 .

[36]  The Effects of Economic Integration Between North and South Korea: A Computable General Equilibrium Analysis , 1997 .

[37]  G. Haberler.  The theory of international trade , 1936 .

[38]  W. Ditto,et al.  Introduction: Control and synchronization of chaos. , 1997, Chaos.

[39]  Erik Mosekilde,et al.  Role of the Absorbing Area in Chaotic Synchronization , 1998 .

[40]  Graham,et al.  The Theory of International Trade , 1989 .

[41]  Laura Gardini,et al.  Role of invariant and minimal absorbing areas in chaos synchronization , 1998 .

[42]  Floris Takens,et al.  Bifurcations and stability of families of diffeomorphisms , 1983 .

[43]  Erik Mosekilde,et al.  Effects of a parameter mismatch on the Synchronization of Two Coupled Chaotic oscillators , 2000, Int. J. Bifurc. Chaos.

[44]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[45]  E. Mosekilde,et al.  TRANSVERSE INSTABILITY AND RIDDLED BASINS IN A SYSTEM OF TWO COUPLED LOGISTIC MAPS , 1998 .

[46]  H. Lorenz.  Nonlinear Dynamical Economics and Chaotic Motion , 1989 .

[47]  T. Puu.  Nonlinear economic dynamics , 1989 .

[48]  O. Popovych,et al.  Desynchronization of chaos in coupled logistic maps. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[49]  Jürgen Kurths,et al.  Transcritical loss of synchronization in coupled chaotic systems , 2000 .