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Hopf bifurcation and stability crossing curves in a cobweb model with heterogeneous producers and time delays
Affiliation:1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;2. College of Mathematic Science, Liaocheng University, Liaocheng 252000, China;1. Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing 210096, PR China;2. Department of Management, Polytechnic University of Marche Piazza Martelli 8, Ancona (AN) I60121, Italy;3. School of Mathematics and Physics, Qingdao University of Science and Technology Qingdao, 266061, PR China;1. Research Center for Complex Systems and Network Sciences, and Department of Mathematics, Southeast University, Nanjing 210096, China;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;5. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Economics and Social Sciences, Catholic University, Via Emilia Parmense 84, 29100 Piacenza, Italy;2. Department of Economics, Quantitative Methods and Management, University of Milano - Bicocca, Piazza Ateneo Nuovo 1, 20126 Milano, Italy;1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;2. School of Computing, Engineering and Mathematics, Western Sydney University, Penrith NSW 2751, Australia;3. School of Economics & Management, Southeast University, Nanjing 210096, China;4. School of Mathematics, Southeast University, Nanjing 210096, China
Abstract:We study a continuous time cobweb model with discrete time delays where heterogeneous producers behave as adapters in the market. Specifically, they partially adjust production (which is subject to some gestation lags) towards the profit-maximising quantity under static expectations. The dynamics of the economy is described by a two-dimensional system of delay differential equations. We characterise stability properties of the stationary state of the system and show the emergence of Hopf bifurcations. We also apply some recent mathematical techniques (stability crossing curves) to show how heterogeneous time delays affect the stability of the economy.
Keywords:Behavioural heterogeneity  Nonlinear cobweb model  Stability crossing curves  Time delays
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