Speeding up population extinction through temporally-modulated and counter-diabatic control

Jaewook Joo

Cleveland Clinic and Case Western Reserve University

"Speeding up population extinction through temporally-modulated and counter-diabatic control"

Stochastic fluctuations are ubiquitous in natural and man-made systems. Those fluctuations can give rise to dramatic, unexpected, and oftentimes catastrophic dynamical consequences such as a sudden population collapse to extinction. Those events are very rare and never happen on a realistic time scale. We are keenly interested in speeding up such a fluctuation-induced rare event of population extinction. We consider a stochastic Verhulst population growth model in a temporally modulated extrinsic condition. In the absence of temporal extrinsic perturbation, the stochastic population system transits to an extinction state along the optimal path which is a heteroclinic orbit connecting the extinction state to the fluctuation-induced state which is created purely due to stochastic fluctuations. When the temporally modulated extrinsic perturbation is turned on, the population extinction accelerates with its mean passage time to extinction being exponentially inversely proportional to the amplitude of temporal modulation. However, such an acceleration is limited only to the small amplitude temporal modulation beyond which the optimal path is disconnected, making the fluctuation-induced extinction implausible. We enforce the connectedness of the optimal path during large amplitude temporal modulation and thus maximally accelerate the population extinction, by using the (quantum) counter-diabatic control that is able to drive the quantum system in a finite time while keeping the system in the quasi-equilibrium state and suppressing non-adiabatic transitions. We extend its application to a tumor growth model with therapy-induced resistance.
Additional authors: N/A

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