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We analyze the stability properties of equilibrium solutions and periodicityof orbits in a two-dimensional dynamical system whose orbits mimic theevolution of the price of an asset and the excess demand for that asset. Theconstruction of the system is grounded upon a heterogeneous interacting agentmodel for a single risky asset market. An advantage of this constructionprocedure is that the resulting dynamical system becomes a macroscopic marketmodel which mirrors the market quantities and qualities that would typically betaken into account solely at the microscopic level of modeling. The system'sparameters correspond to: (a) the proportion of speculators in a market; (b)the traders' speculative trend; (c) the degree of heterogeneity ofidiosyncratic evaluations of the market agents with respect to the asset'sfundamental value; and (d) the strength of the feedback of the populationexcess demand on the asset price update increment. This correspondence allowsus to employ our results in order to infer plausible causes for the emergenceof price and demand fluctuations in a real asset market.  The employment of dynamical systems for studying evolution of stochasticmodels of socio-economic phenomena is quite usual in the area of heterogeneousinteracting agent models. However, in the vast majority of the cases present inthe literature, these dynamical systems are one-dimensional. Our work is amongthe few in the area that construct and study two-dimensional dynamical systemsand apply them for explanation of socio-economic phenomena.

Stability analysis with applications of a two-dimensional dynamical system arising from a stochastic model of an asset market