-
Previous Article
Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model
- DCDS-B Home
- This Issue
-
Next Article
Dynamic bifurcation theory of Rayleigh-Bénard convection with infinite Prandtl number
Analysis of a nonlinear system for community intervention in mosquito control
| 1. | Department of Mathematics, Bentley College, 175 Forest Street, Waltham, MA 02452, United States |
| 2. | Department of Population and International Health, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA 02115, United States, United States |
$x_{n+1}= a x_{n}h(p y_{n})+b h(q y_{n})$
n=0,1,...
$y_{n+1}= c x_{n}+d y_{n}$
where the function $h\in C^{1}$ ( [ $0,\infty$) $\to $ [$0,1$] ) satisfying certain properties, will denote either $h(t)=h_{1}(t)=e^{-t}$ and/or $h(t)=h_{2}(t)=1/(1+t).$ We give conditions in terms of parameters for boundedness and stability. This enables us to explore the dynamics of prevalence/community-activity systems as affected by the range of parameters.
| [1] |
Kai Liu, Zhi Li. Global attracting set, exponential decay and stability in distribution of neutral SPDEs driven by additive $\alpha$-stable processes. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3551-3573. doi: 10.3934/dcdsb.2016110 |
| [2] |
Hal L. Smith, Horst R. Thieme. Persistence and global stability for a class of discrete time structured population models. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4627-4646. doi: 10.3934/dcds.2013.33.4627 |
| [3] |
Nguyen Thieu Huy, Vu Thi Ngoc Ha, Pham Truong Xuan. Boundedness and stability of solutions to semi-linear equations and applications to fluid dynamics. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2103-2116. doi: 10.3934/cpaa.2016029 |
| [4] |
Ö. Uğur, G. W. Weber. Optimization and dynamics of gene-environment networks with intervals. Journal of Industrial and Management Optimization, 2007, 3 (2) : 357-379. doi: 10.3934/jimo.2007.3.357 |
| [5] |
Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure and Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002 |
| [6] |
Kazuo Yamazaki, Xueying Wang. Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 559-579. doi: 10.3934/mbe.2017033 |
| [7] |
Fuchen Zhang, Xiaofeng Liao, Chunlai Mu, Guangyun Zhang, Yi-An Chen. On global boundedness of the Chen system. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1673-1681. doi: 10.3934/dcdsb.2017080 |
| [8] |
Qi Wang, Yang Song, Lingjie Shao. Boundedness and persistence of populations in advective Lotka-Volterra competition system. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2245-2263. doi: 10.3934/dcdsb.2018195 |
| [9] |
Cemil Tunç. Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations. Conference Publications, 2011, 2011 (Special) : 1395-1403. doi: 10.3934/proc.2011.2011.1395 |
| [10] |
Pierre Magal. Global stability for differential equations with homogeneous nonlinearity and application to population dynamics. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 541-560. doi: 10.3934/dcdsb.2002.2.541 |
| [11] |
Guihong Fan, Yijun Lou, Horst R. Thieme, Jianhong Wu. Stability and persistence in ODE models for populations with many stages. Mathematical Biosciences & Engineering, 2015, 12 (4) : 661-686. doi: 10.3934/mbe.2015.12.661 |
| [12] |
Marcel Freitag. Global existence and boundedness in a chemorepulsion system with superlinear diffusion. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5943-5961. doi: 10.3934/dcds.2018258 |
| [13] |
Vincent Calvez, Lucilla Corrias. Blow-up dynamics of self-attracting diffusive particles driven by competing convexities. Discrete and Continuous Dynamical Systems - B, 2013, 18 (8) : 2029-2050. doi: 10.3934/dcdsb.2013.18.2029 |
| [14] |
Răzvan M. Tudoran. Dynamical systems with a prescribed globally bp-attracting set and applications to conservative dynamics. Discrete and Continuous Dynamical Systems, 2020, 40 (5) : 3013-3030. doi: 10.3934/dcds.2020159 |
| [15] |
Evariste Sanchez-Palencia, Jean-Pierre Françoise. Topological remarks and new examples of persistence of diversity in biological dynamics. Discrete and Continuous Dynamical Systems - S, 2019, 12 (6) : 1775-1789. doi: 10.3934/dcdss.2019117 |
| [16] |
Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. Mathematical Biosciences & Engineering, 2015, 12 (4) : 859-877. doi: 10.3934/mbe.2015.12.859 |
| [17] |
Cyrine Fitouri, Alain Haraux. Boundedness and stability for the damped and forced single well Duffing equation. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 211-223. doi: 10.3934/dcds.2013.33.211 |
| [18] |
Mengyao Ding, Wei Wang. Global boundedness in a quasilinear fully parabolic chemotaxis system with indirect signal production. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4665-4684. doi: 10.3934/dcdsb.2018328 |
| [19] |
Wei Wang, Yan Li, Hao Yu. Global boundedness in higher dimensions for a fully parabolic chemotaxis system with singular sensitivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3663-3669. doi: 10.3934/dcdsb.2017147 |
| [20] |
Hao Yu, Wei Wang, Sining Zheng. Global boundedness of solutions to a Keller-Segel system with nonlinear sensitivity. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1317-1327. doi: 10.3934/dcdsb.2016.21.1317 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]