Bifurcations in a stock market model. (English) Zbl 0759.90011
Summary: A theoretical framework is laid out, where a Stock Exchange is represented as a process under decentralized control. Attention is devoted to a specific case, in which the trading activity is described by a second order dynamical system. Three economically significant modes of behavior are identified. The stock market can (1) adjust to a stable equilibrium, (2) approach a stable limit cycle, (3) diverge to infinity. The transition from mode (1) to mode (2) is a supercritical Hopf bifurcation, whereas the transition from mode (2) to mode (3) is a homoclinic bifurcation.
MSC:
| 91B62 | Economic growth models |
| 93C10 | Nonlinear systems in control theory |
| 34C23 | Bifurcation theory for ordinary differential equations |
Keywords:
stability; stock exchange; process under decentralized control; second order dynamical system; stable equilibrium; stable limit cycle; supercritical Hopf bifurcationSoftware:
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