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Theory and Modern Applications

Table 2 Impulsive and phase sets of system (1)

From: The impact of resource limitation on the pest-natural enemy ecosystem with anti-predator behavior and fear effect

Case

ET

(1 − θ)ET

\(\mathcal{M}_{s}\)

\(\mathcal{N}_{s}\)

 

(a)

   

\(\mathcal{N}_{1}\)

\(J_{21}\)

(b)

\(ET>x^{*}\)

\((1-\theta )ET< x_{3}\)

\(\mathcal{M}_{1}\)

\(\mathcal{N}_{2}\)

 

(c)

   

\(\mathcal{N}_{3}\)

 

(d)

   

\(\mathcal{N}_{4}\)

\(J_{22}\)

(e)

\(ET>x^{*}\)

\((1-\theta )ET \geq x_{3}\)

\(\mathcal{M}\)

\(\mathcal{N}_{5}\)

 

(f)

   

\(\mathcal{N}_{6}\)