We analyze the stability properties of equilibrium solutions and periodicity
of orbits in a two-dimensional dynamical system whose orbits mimic the
evolution of the price of an asset and the excess demand for that asset. The
construction of the system is grounded upon a heterogeneous interacting agent
model for a single risky asset market. An advantage of this construction
procedure is that the resulting dynamical system becomes a macroscopic market
model which mirrors the market quantities and qualities that would typically be
taken into account solely at the microscopic level of modeling. The system's
parameters correspond to: (a) the proportion of speculators in a market; (b)
the traders' speculative trend; (c) the degree of heterogeneity of
idiosyncratic evaluations of the market agents with respect to the asset's
fundamental value; and (d) the strength of the feedback of the population
excess demand on the asset price update increment. This correspondence allows
us to employ our results in order to infer plausible causes for the emergence
of price and demand fluctuations in a real asset market.

The employment of dynamical systems for studying evolution of stochastic
models of socio-economic phenomena is quite usual in the area of heterogeneous
interacting agent models. However, in the vast majority of the cases present in
the literature, these dynamical systems are one-dimensional. Our work is among
the few in the area that construct and study two-dimensional dynamical systems
and apply them for explanation of socio-economic phenomena.