Homoclinic and Heteroclinic Motions in Economic Models with Exogenous Shocks

Abstract In this study, we theoretically prove the presence of homoclinic and heteroclinic motions in the dynamics of economic models perturbed with exogenous shocks. An illustrative example based on the Kaldor model of the aggregate economy is presented.

[1]  Marat Akhmet,et al.  Replication of Chaos in Neural Networks, Economics and Physics , 2015 .

[2]  M. Akhmet.  Homoclinical structure of the chaotic attractor , 2010 .

[3]  M. Akhmet.  Devaney’s chaos of a relay system , 2009 .

[4]  Wei-Bin Zhang.  Differential Equations, Bifurcations and Chaos in Economics , 2005 .

[5]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[6]  Marat Akhmet,et al.  Exogenous Versus Endogenous for Chaotic Business Cycles , 2015 .

[7]  M. O. Fen,et al.  Shunting inhibitory cellular neural networks with chaotic external inputs. , 2013, Chaos.

[8]  Marcel Ausloos,et al.  The logistic map and the route to chaos : from the beginnings to modern applications , 2006 .

[9]  L. Gardini,et al.  Homoclinic bifurcations in heterogeneous market models , 2003 .

[10]  Walter C. Labys,et al.  Evidence of chaos in commodity futures prices , 1992 .

[11]  M. Akhmet.  The complex dynamics of the cardiovascular system , 2009 .

[12]  M. Feigenbaum.  Universal behavior in nonlinear systems , 1983 .

[13]  Marat Akhmet,et al.  Chaos in economic models with exogenous shocks , 2014 .

[14]  M. Yokoo,et al.  Chaotic dynamics in a two-dimensional overlapping generations model , 2000 .

[15]  M. O. Fen,et al.  Replication of Discrete Chaos , 2014 .

[16]  Marat Akhmet,et al.  Replication of chaos , 2013, Commun. Nonlinear Sci. Numer. Simul..

[17]  M. U. Akhmet,et al.  Entrainment by Chaos , 2012, J. Nonlinear Sci..

[18]  Andrea L. Bertozzi,et al.  Heteroclinic orbits and chaotic dynamics in planar fluid flows , 1988 .

[19]  Marat Akhmet,et al.  Nonlinear Hybrid Continuous/Discrete-Time Models , 2011 .

[20]  L. P. Šil'nikov.  ON A POINCARÉ-BIRKHOFF PROBLEM , 1967 .

[21]  Antje Sommer.  Nonlinear Dynamical Economics And Chaotic Motion , 2016 .

[22]  Laura Gardini,et al.  Calculation of homoclinic and heteroclinic orbits in 1D maps , 2015, Commun. Nonlinear Sci. Numer. Simul..

[23]  M. O. Fen,et al.  Extension of spatiotemporal chaos in glow discharge-semiconductor systems. , 2014, Chaos.

[24]  J. Hale,et al.  Dynamics and Bifurcations , 1991 .

[25]  R. Leuthold,et al.  Long Agricultural Futures Prices: Arch, Long Memory, or Chaos Processes , 1998 .

[26]  L. Shilnikov,et al.  Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits. , 1996, Chaos.

[27]  Marat Akhmet,et al.  Attraction of Li-Yorke chaos by retarded SICNNs , 2015, Neurocomputing.

[28]  S. Smale.  Diffeomorphisms with Many Periodic Points , 1965 .

[29]  Laura Gardini,et al.  Homoclinic tangles in a Kaldor-like business cycle model , 2007 .

[30]  Marat Akhmet,et al.  Li-Yorke chaos in the system with impacts , 2009 .

[31]  K. G. Andersson.  Poincaré's discovery of homoclinic points , 1994 .

[32]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[33]  R. Chacón,et al.  Homoclinic and heteroclinic chaos in a triple-well oscillator , 1995 .

[34]  A. Naimzada,et al.  Dynamic effects of increasing heterogeneity in financial markets , 2009 .

[35]  Epaminondas Panas,et al.  Are oil markets chaotic? A non-linear dynamic analysis , 2000 .

[36]  P. Hartman.  Ordinary Differential Equations , 1965 .

[37]  A. Agliari,et al.  Homoclinic and Heteroclinic Bifurcations in an Overlapping Generations Model with Credit Market Imperfection , 2011 .