Geodesic
Scenario of the invasive process in the modification of Bazykins population equation with delayed regulation and high reproductive potential
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 91-102

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The paper discusses modeling of the variant of the development of a rapid invasive process in competitive biosystems. The emergence of dangerous alien species leads to extreme phenomena in the dynamics of populations. Invasions generate a phase of active spread of the alien species, but outbreaks are often followed by a phase of sharp depression. Changes in the process are associated with active resistance, which has a delayed activation time interval and a threshold level of maximizing the impact $J$. For the mathematical formalization of the successively following stages of the outbreak/crisis, equations with a deviating argument are used. In a variant of the equation with a delayed tuning of the biotic reaction $\dot x=rf(x(t-\tau))-\mathfrak{F}(x^m(t-\nu);J)$ a variant of the passage of the crisis that occurs it is in the phase of rapid growth until a balance is reached with the resources of the environment. Due to the threshold feedback, the competitive pressure after a deep crisis is weakened and the invasive population goes into a mode of damped oscillations. The asymptotic level of equilibrium in the scenario with a crisis turns out to be much less than the theoretically permissible limiting level of abundance for an alien species in a given environment. The new Equation also has an interpretation to describe the weakening development of the immune response in a situation of chronicity of the infectious process.
Keywords: modeling of extreme events, threshold effects, equations with delay, nonlinear ecological regulation. 
A. Yu. Perevaryukha. Scenario of the invasive process in the modification of Bazykins population equation with delayed regulation and high reproductive potential. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 91-102. http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a6/
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