Necessary Conditions For Global Stability Research Articles

Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations

To suppress wild population of Aedes mosquitoes, the primary transmission vector of life-threatening diseases such as dengue, malaria, and Zika, an innovative strategy is to release male mosquitoes carrying the bacterium Wolbachia into natural areas to drive female sterility by cytoplasmic incompatibility. We develop a model of delay differential equations, incorporating the strong density restriction in the larval stage, to assess the delicate impact of life table parameters on suppression efficiency. Through mathematical analysis, we find the sufficient and necessary condition for global stability of the complete suppression state. This condition, combined with the experimental data for Aedes albopictus population in Guangzhou, helps us predict a large range of releasing intensities for suppression success. In particular, we find that if the number of released infected males is no less than four times the number of mosquitoes in wild areas, then the mosquito density in the peak season can be reduced by 95%. We introduce an index to quantify the dependence of suppression efficiency on parameters. The invariance of some quantitative properties of the index values under various perturbations of the same parameter justifies the applicability of this index, and the robustness of our modeling approach. The index yields a ranking of the sensitivity of all parameters, among which the adult mortality has the highest sensitivity and is considerably more sensitive than the natural larvae mortality.

Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer

Advanced prostate cancer is often treated by androgen deprivation therapy, which is initially effective but gives rise to fatal treatment-resistant cancer. Intermittent androgen deprivation therapy improves the quality of life of patients and may delay resistance towards treatment. Immunotherapy alters the bodies immune system to help fight cancer and has proven effective in certain types of cancer. We propose a model incorporating androgen deprivation therapy (intermittent and continual) in conjunction with dendritic cell vaccine immunotherapy. Simulations are run to determine the sensitivity of cancer growth to dendritic cell vaccine therapy administration schedule. We consider the limiting case where dendritic cells are administered continuously and perform analysis on the full model and the limiting cases of the model to determine necessary conditions for global stability of cancer eradication.

Sufficient and necessary conditions for global stability of genetic regulator networks with time delays

This paper is concerned with the global stability of the nonlinear model for genetic regulator networks (GRNs) with time delays. Four new sufficient and necessary conditions for global asymptotic stability and global exponential stability of the equilibrium point of GRNs are derived. Specifically, using comparing theorem and Dini derivation method, three weak sufficient conditions for global stability of GRNs with constant time delays are proposed. Finally, a general GRN model is used to illustrate the effectiveness of the proposed theoretical results. Compared with the previous results, some sufficient and necessary conditions for Lyapunov stability of GRNs are proposed, which are not seen before.

Pattern formation in prey-taxis systems

In this paper, we consider spatial predator–prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey. We identify combinations of the above non-linearities that lead to spatial pattern formation and we give numerical examples. It turns out that prey-taxis stabilizes the system and for large prey-taxis sensitivity we do not observe pattern formation. We also study and find necessary conditions for global stability for a type I functional response, logistic growth for the prey, non-linear predator death terms, and non-linear prey-taxis sensitivity.

Bifurcation Control of Aeroelastic Limit Cycle Oscillations

An active flutter suppression using linear saturated control is investigated for a 2dof wing section with nonlinear torsional stiffness and limited deflection amplitude of its single control effector. The suppression of limit cycle oscillations in the nonlinear closed-loop system is achieved through maximization of the stability region of the linearized system. A bifurcation sequence leading to limit cycle disappearance is revealed. With increase of the maximum control input amplitude, the closed-loop limit cycle is transformed into a stable torus, which disappears at higher control amplitude through a nonlocal bifurcation similar to a boundary crisis in chaotic systems. Finally, a saddle-node bifurcation of the limit cycle gives necessary conditions for global stability in the closed-loop system.

Necessary conditions for global stability of multiclass queueing networks

In this paper, we obtain necessary conditions for the global stability of a d-station multiclass queueing network. The conditions are given explicitly in terms of the average service and arrival rates of the network. Although these conditions are in general not sufficient for d > 2, they may still highlight hidden bottlenecks in complex manufacturing systems such as wafer fabrication processes.