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**Stability, chaos and multiple attractors: a single agent makes a difference.**
*(English)*
Zbl 1178.91105

Summary: This paper provides an example in which a slight behavioral heterogeneity may fundamentally change the dynamical properties of a nonlinear cobweb market with a quadratic cost function and an isoelastic demand function. We consider two types of producers; cautious adapters and naive optimizers. In a market of naive optimizers a single cautious adapter stabilizes the otherwise exploding market. In a market of cautious adapters a single naive optimizer may destabilize the market; without him there exists at most one periodic attractor in the market but with him there may appear many (and even infinitely many) coexisting periodic attractors.

### MSC:

91B55 | Economic dynamics |

37N40 | Dynamical systems in optimization and economics |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

### Keywords:

2-D nonlinear cobweb model; behavioral heterogeneity; chaos; homoclinic bifurcations; coexisting periodic attractors
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\textit{T. Onozaki} et al., J. Econ. Dyn. Control 27, No. 10, 1917--1938 (2003; Zbl 1178.91105)

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