Equilibrium, pseudoequilibrium and sliding-mode heteroclinic orbit in a Filippov-type plant disease model. (October 2016)

• Record Type: Journal Article
• Authors: Wang, Jiafu; Zhang, Fengqin; Wang, Lin
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 308
• Page End: 324
• Publication Date: 2016-10
• Subjects: Equilibrium -- Pseudoequilibrium -- Sliding-mode heteroclinic orbit -- Filippov system -- Non-smooth Lyapunov function -- Global dynamics; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.017
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Plant diseases have caused tremendous crop losses and have massive impacts on food security and environment. Modeling the spread of plant diseases and understanding the dynamics of the resulting plant disease models may provide practical insights on designing effective control measures. In this paper, by incorporating cultural strategies and economic threshold policy, we present a Filippov-type plant disease model. The resulting model has state dependent discontinuous right-hand side and thus non-smooth analysis and generalized Lyapunov approach are employed for model analysis. We show that the model exhibits the phenomena of stable equilibrium, unstable pseudoequilibrium as well as sliding-mode heteroclinic orbit. Biological implications of our results in implementing control strategies for plant diseases are also discussed. Highlights: A Filippov-type plant disease model that incorporates cultural strategies and economic threshold policy is studied. To deal with the resulting non-smooth system, the generalized Lyapunov approach is employed. Our model is shown to admit stable equilibrium, unstable pseudoequilibrium and sliding-mode heteroclinic orbit. Biological implications in implementing control strategies for plant diseases are discussed.