  In this paper we study a nonlinear age structured model of locust population
dynamics with variable time of egg incubation that describes the phase
polyphenism and behaviour of desert locust, Schistocerca gregaria. The analysis
of asymptotical stability of trivial and nontrivial equilibriums of autonomous
system allows us to derive the conditions and understand the particularities of
bidirectional phase transitions between solitarious and gregarious. Simulation
of locust population dynamics with different conditions of phase transitions
for autonomous and non-autonomous dynamical systems of our two phase
age-structured competitive model with time delay exhibits the features of
behaviour of documented outbreak dynamics of Schistocerca gregaria.
