The core oscillator of the Arabidopsis circadian clock model consists of multiple interlocked transcription-translation feedback loops. It is crucial to effectively identify the internal core regulatory factors for understanding the complex mechanisms of plant circadian rhythms. This work simulates the circadian rhythm clock of Arabidopsis through a moderately complex system of ordinary differential equations, where 30 parameters in the model are evaluated to quantify their impact on circadian rhythm characteristics using the Sobol' method. The results indicate that the key parameters affecting the oscillation characteristics of the circadian clock are closely related to specific regulatory pathways, and some parameters exhibit amplitude sensitivity or period sensitivity. Sensitive parameters are dispersed throughout the entire system, while key control parameters are concentrated in the EL-P97-CL pathway, particularly in terms of the degradation rate. Sensitivity analysis of parameter classes indicates that degradation rate and kinase binding strength have a significant impact on the period and amplitude. Finally, we compare the sensitivity analysis results of the recently updated model with those of the original model. The results indicate that constructing the core structure around P97-CL ensures the accuracy and robustness of circadian rhythms. These findings elucidate the role of key parameters in the dynamics of circadian rhythms and deepen our understanding of their regulatory mechanisms.
Hepatitis C virus (HCV) is a major global health concern caused by a blood-borne viral infection that primarily targets the liver. Due to the difficulty of obtaining accurate parameter estimates in epidemiological systems, we incorporate parameter uncertainty into the modeling framework by means of a stochastic imprecise differential system. In this work, we investigate a treatment strategy for an HCV stochastic model under environmental fluctuations and parameter imprecision. We establish the existence and positivity of the global solution. By using Lyapunov function techniques and stochastic stability theory, we derive sufficient conditions for both extinction and persistence of the disease, expressed in terms of a stochastic threshold & Rscr;(s). Furthermore, we formulate a near-optimal control problem in a non-convex control setting and obtain a priori estimates for admissible controls. By applying Ekeland's variational principle together with the stochastic Hamiltonian maximum condition, we derive necessary and sufficient conditions for near-optimality of the control problem. Finally, numerical simulations are provided to illustrate and support the theoretical results.
Due to fear of predation, prey populations adopt various anti-predator defense strategies, which reduce their birth rate. Here, we formulate both autonomous and non-autonomous prey-predator systems with the assumptions that the prey's per capita birth rate decreases as a consequence of fear of predators, and that predator species waste time searching for prey species due to encounters with other predators. For the autonomous system, we establish the criteria under which the system is uniformly persistent and those under which the coexistence equilibrium point is globally asymptotically stable. Moreover, the existence of local bifurcations, one- and two-parameter bifurcation analyses, and the influence of each ecological parameter on system dynamics are rigorously examined. For the non-autonomous system, we establish the conditions for uniform persistence and prove the existence of a unique globally asymptotically stable periodic solution under certain conditions.
This paper considers a chemostat system with a consumer and a resource. The consumer moves between multiple sink-source patches with both resource and toxicant. By using graph-theoretic method and Lyapunov theory, we show global stability of positive equilibria in the system. Rigorous analysis on the equilibria demonstrates that diffusion could make the consumer persist in sinks and even make the total population abundance larger than that without diffusion. Asymmetry in diffusion, toxicant distribution, and spatial pattern of patches play crucial roles in the persistence and increase, while two formulas are deduced for total abundances with/without diffusion. On the contrary, diffusion could also lead to decrease of the total abundance, even lead to extinction of the consumer in sources. Our results are consistent with empirical observations, and provide new insights. This work is important for both conservation of endangered species and control of pests.
A stochastic predator-prey system with Markov switching and colored noise is studied, where Markov switching is used to represent parameter changes caused by environmental mutations. The joint impact of switching and colored noise on the stationary response is explored by the stochastic averaging method, the stochastic Runge-Kutta algorithm, and the most probable trajectory theory. Findings show that a wider bandwidth tends to make the stationary response more concentrated and drives the most probable response closer to the deterministic one, whereas a narrower bandwidth is associated with stronger population oscillations. A larger stationary probability tends to drive the system response toward that of the corresponding substate, while a faster transition rate generally stabilizes the most probable response. In addition, both the bandwidth parameter and switching may induce stochastic P-bifurcation, accompanied by changes in the concentration and shape of the stationary distribution. The results also indicate that the overall stationary response is influenced not only by stationary probabilities but also by the intrinsic stability of the substates.
