In this paper, we study the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of linear growth and nonlinear function. Both the classical reaction-diffusion equation and nonlocal dispersal equation are investigated. Our main results reveal that the linear and nonlinear parts of reaction term play quite different roles in the study of positive solutions.

This paper deals with the logistic Keller–Segel model

\[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ v_t = \Delta v - v + u \end{cases} \]

$\bar {\Omega }\times (0,\infty )$

Field studies were conducted in southern Ontario to determine the critical period of weed control in grain corn and the influence of weed interference on corn leaf area. The Gompertz and logistic equations were fitted to data representing increasing durations of weed control and weed interference, respectively. The beginning of the critical period varied from the 3- to 14-leaf stages of corn development However, the end of the critical period was less variable and ended on average at the 14-leaf stage. Weed interference reduced corn leaf area by reducing the expanded leaf area of each individual leaf and accelerating senescence of lower leaves. In addition, weed interference up to the 14-leaf stage of corn development impeded leaf expansion and emergence in 1989.

The effect of weed interference on corn yield and the critical period for weed control (CPWC) were determined in Germany and Benin. Treatments with weed control starting at different crop growth stages and continuously kept weed-free until harvest represented the “weed-infested interval.” Treatments that were kept weed-free from sowing until different crop growth stages represented the “weed-free interval.” Michaelis–Menten, Gompertz, logistic and log–logistic models were employed to model the weed interference on yield. Cross-validation revealed that the log–logistic model fitted the weed-infested interval data equally well as the logistic and slightly better than the Gompertz model fitted the weed-free interval. For Benin, economic calculations considered yield revenue and cost increase due to mechanical weeding operations. Weeding once at the ten-leaf stage of corn resulted already profitable in three out of four cases. One additional weeding operation may optimize and assure profit. Economic calculations for Germany determined a CPWC starting earlier than the four-leaf stage, challenging the decade-long propagated CPWC for corn. Differences between Germany and Benin are probably due to the higher yields and high costs in Germany. This study provides a straightforward method to implement economic data in the determination of the CPWC for chemical and nonchemical weed control strategies.

This paper explores the influence of demographic and spatial variables on individual participation and consumption of wildland area recreation. Data from the National Survey on Recreation and the Environment are combined with geographical information system-based distance measures to develop nonlinear regression models used to predict both participation and the number of days of participation in wilderness and primitive area recreation. The estimated models corroborate previous findings indicating that race (black), ethnicity (Hispanic), immigrant status, age, and urban dwelling are negatively correlated with wildland visitation, while income, gender (male), and education positively affect wild-land recreation participation and use. The presence of a distance or proximity factor mitigates some of the influence of race and ethnicity. The results of the cross-sectional models are combined with U.S. Census projections of total population, changes in population characteristics, and estimates of current National Forest Wilderness visitation estimates to give some insight into pressure that might be expected on the nation's designated wilderness during the next half century. Results generally indicate that per-capita participation and visitation rates will decline over time as society changes. Total wilderness participation and visitation will, however, increase, but at a rate less than population growth.