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Theory and Modern Applications

Figure 3 | Advances in Difference Equations

Figure 3

From: Mathematical modeling of rhizosphere microbial degradation with impulsive diffusion on nutrient

Figure 3

Dynamical behavior of the system ( 2.1 ) with \(\pmb{Q=0.8}\) , \(\pmb{N^{0}=20}\) , \(\pmb{D=0.1}\) , \(\pmb{\mu=0.3}\) , \(\pmb{\delta=0.1}\) , \(\pmb{K=1.8}\) , \(\pmb{m=0.1}\) , \(\pmb{d=0.0001}\) , \(\pmb{N_{1}(0)=18}\) , \(\pmb{N_{2}(0)=0.2}\) , \(\pmb{x(0)=0.1}\) , \(\pmb{R=15.99>1}\) . (a) Time-series of the nutrient concentration outside the rhizosphere (patch 2). (b) Time-series of the nutrient concentration inside the rhizosphere (patch 1). (c) Phase portrait implying system (2.1) is permanent for \(R>1\).

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