Ja. Holyst et al., DESTRUCTIVE ROLE OF COMPETITION AND NOISE FOR CONTROL OF MICROECONOMICAL CHAOS, Chaos, solitons and fractals, 8(9), 1997, pp. 1489-1505
The problem of control of chaos in a microeconomical mode! describing
two competing firms with asymmetrical investment strategies is studied
. Cases when both firms try to perform the control simultaneously or w
hen noise is present are considered, For the first case the resulting
control efficiency depends on the system parameters and on the maximal
values of perturbations of investment parameters for each firm, Analy
tic calculations and numerical simulations show that competition in th
e control leads to 'parasitic' oscillations around the periodic orbit
that can destroy the expected stabilization effect. The form of these
oscillations is dependent on non-linear terms describing the motion ar
ound periodic orbits. An analytic condition for stable behaviour of th
e oscillation (i.e. the condition for control stability) is found. The
values of the mean period of these oscillations is a decreasing funct
ion of the amplitude of investment perturbation of the less effective
firm. On the other hand, amplitudes of market oscillations are increas
ing functions of this parameter. In the presence of noise the control
can be also successful provided the amplitude of allowed investment ch
anges is larger than some critical threshold which is proportional to
the maximal possible noise value. In the case of an unbounded noise, t
he time of laminar epochs is always finite but their mean length incre
ases with the amplitude of investment changes. Computer simulations ar
e in very good agreement with analytical results obtained for this mod
el. (C) 1991 Elsevier Science Ltd.