Continuous Model for the Devastating Oscillation Dynamics of Local Forest Pest Populations in Canada*
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A sharp and prolonged change in developing population processes requires mathematical methods to be improved. Unusual phase changes in the development of mass reproduction of insect species stipulated the idea to develop a new model in which not the final form of an asymptotically stable state after bifurcations but transient modes are of importance. In concrete situations, it is proposed to consider the phenomena, which are identified with population outbreaks (non-stationary heterogeneous processes) in environmental studies, within the context of a long oscillatory mode only as peaks of the phases of sharp nonharmonic oscillations. The proposed new dynamic model in the form of a differential equation describes a decreasing pseudoperiodic damping trajectory of sudden sharp oscillations that implement a non-bifurcation scenario of spontaneous completion for a particular variant of mass forest pest reproduction. Situations in two provinces of eastern Canada are considered as examples.
Keywordscontinuous model of population explosive dynamics of an insect outbreak transient oscillation mode cycle damping forest pest outbreak in Canada
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