Bifurcation and Chaos in a Price Game of Irrigation Water in a Coastal Irrigation District

We propose a price game model of irrigation water in a coastal irrigation district. Then, we discuss the stability and codimension-two period-doubling (flip) bifurcation. Then, the MATLAB package Cl_MatContM is employed to illustrate its numerical bifurcations-based continuation methods. Lastly, the 0-1 test algorithm is used to compute the median value of correlation coefficient which can indicate whether the underlying dynamics is regular or chaotic.

[1]  Wouter J. Den Haan,et al.  The importance of the number of different agents in a heterogeneous asset-pricing model , 2001 .

[2]  Avinash Dixit,et al.  Comparative Statics for Oligopoly , 1986 .

[3]  George P. Papavassilopoulos,et al.  An Adaptive Learning Game Model for Interacting Electric Power Markets , 2010, INFOR Inf. Syst. Oper. Res..

[4]  R. Baldick,et al.  Short-term electricity market auction game analysis: uniform and pay-as-bid pricing , 2004, IEEE Transactions on Power Systems.

[5]  Weihong Huang,et al.  The long-run benefits of chaos to oligopolistic firms , 2008 .

[6]  Ronald C. Griffin,et al.  Water Resource Economics: The Analysis of Scarcity, Policies, and Projects , 2005 .

[7]  Baogui Xin,et al.  On a master–slave Bertrand game model , 2011 .

[8]  Q. Da,et al.  The dynamics of Bertrand model with bounded rationality , 2009 .

[9]  Irrigation Water Pricing: The Gap Between Theory and Practice , 2010 .

[10]  Michael Kopel,et al.  Simple and complex adjustment dynamics in Cournot duopoly models , 1996 .

[11]  Willy Govaerts,et al.  Numerical Methods for Two-Parameter Local Bifurcation Analysis of Maps , 2007, SIAM J. Sci. Comput..

[12]  A. Dinar,et al.  Pricing irrigation water: a review of theory and practice , 2002 .

[13]  A. A. Elsadany,et al.  Nonlinear dynamics in the Cournot duopoly game with heterogeneous players , 2003 .

[14]  Qigui Yang,et al.  A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions , 2011 .

[15]  Wouter J. Denhaan.  The Importance Of The Number Of Different Agents In A Heterogeneous Asset-Pricing Model , 2000 .

[16]  Duopoly in the Japanese Airline Market: Bayesian Estimation for the Entry Game , 2012 .

[17]  Tönu Puu,et al.  Chaos in business cycles , 1991 .

[18]  Junhai Ma,et al.  Complexity of triopoly price game in Chinese cold rolled steel market , 2012 .

[19]  W. Govaerts,et al.  Resonance and bifurcation in a discrete-time predator–prey system with Holling functional response , 2012 .

[20]  A. A. Elsadany,et al.  Competition analysis of a triopoly game with bounded rationality , 2012 .

[21]  Georg A. Gottwald,et al.  On the validity of the 0–1 test for chaos , 2009, 0906.1415.

[22]  Gian Italo Bischi,et al.  Equilibrium selection in a nonlinear duopoly game with adaptive expectations , 2001 .

[23]  Guilin Wen,et al.  Criterion to identify Hopf bifurcations in maps of arbitrary dimension. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  E. Allgower,et al.  Numerical Continuation Methods , 1990 .

[25]  Tingwen Huang,et al.  Analysis of decision-making in economic chaos control , 2009 .

[26]  Kjetil Wormnes,et al.  Application of the 0-1 Test for Chaos to Experimental Data , 2007, SIAM J. Appl. Dyn. Syst..

[27]  Konstantinos G. Gkonis,et al.  The LNG Market: A Game Theoretic Approach to Competition in LNG Shipping , 2009 .

[28]  Guilin Wen,et al.  On creation of Hopf bifurcations in discrete-time nonlinear systems. , 2002, Chaos.

[29]  Junhai Ma,et al.  Price game and chaos control among three oligarchs with different rationalities in property insurance market. , 2012, Chaos.

[30]  Lingling Mu,et al.  A 3-dimensional discrete model of housing price and its inherent complexity analysis , 2009, J. Syst. Sci. Complex..

[31]  Dawei Xu,et al.  Complexity of discrete investment competition model based on heterogeneous participants , 2012, Int. J. Comput. Math..

[32]  刘璇,et al.  The 0-1 test algorithm for chaos and its applications , 2010 .

[33]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[34]  Fabio Tramontana,et al.  Heterogeneous triopoly game with isoelastic demand function , 2012 .

[35]  W. Govaerts,et al.  Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems , 2011 .

[36]  Willy Govaerts,et al.  Stable cycles in a Cournot duopoly model of Kopel , 2008 .

[37]  W. Douglass Shaw,et al.  Water Resource Economics and Policy: An Introduction , 2005 .

[38]  G. Bischi,et al.  Oligopoly games with Local Monopolistic Approximation , 2007 .

[39]  Jinzhu Zhang,et al.  Complexity of a Real Estate Game Model with a nonlinear Demand Function , 2011, Int. J. Bifurc. Chaos.

[40]  Terry L. Friesz,et al.  Oligopolies in pollution permit markets: A dynamic game approach , 2012 .

[41]  Laura Gardini,et al.  Cournot duopoly when the competitors operate multiple production plants , 2009 .

[42]  Fabio Tramontana,et al.  Heterogeneous duopoly with isoelastic demand function , 2010 .

[43]  R. Meinzen-Dick.  Beyond panaceas in water institutions , 2007, Proceedings of the National Academy of Sciences.

[44]  Georg A. Gottwald,et al.  On the Implementation of the 0-1 Test for Chaos , 2009, SIAM J. Appl. Dyn. Syst..

[45]  W. Ji.  Chaos and Control of Game Model Based on Heterogeneous Expectations in Electric Power Triopoly , 2009 .

[46]  Bingyong Tang,et al.  Minority game and anomalies in financial markets , 2004 .

[47]  Baogui Xin,et al.  Complex Dynamics of an Adnascent-Type Game Model , 2008 .

[48]  Ian Melbourne,et al.  Comment on "Reliability of the 0-1 test for chaos". , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.