Linear Control Systems

Ratio-dependent predator–prey model: effect of environmental fluctuation and stability

“…Hence system (2.5) is dissipative with the asymptotic bound L/c. This ensures the existence of a compact neighbourhood which is a proper subset of R 2 + such that for sufficiently large initial conditions (x 0 , y 0 ) the trajectories of the system of equations (2.5) will always be within the set .…”

“…where A denotes the coefficient matrix of linear part with zero as the main diagonal elements; B(u, v), C(u, v, w) are symmetric multi-linear vector functions of u 2 and take the following forms: where the c ij (i = 1, 2; j = 1, 2, 3, 4) are given by…”

“…Let be the set defined by = [(t t 0 ) × R 2 , t 0 ∈ R + ]. Let V ∈ C 2 ( ) be a twice differentiable function of time t. We define the following theorem due to Afanas'ev et al [2].…”