Analysis on existence of bifurcation solutions for a predator-prey model with herd behavior

Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping

“…In this case, the number of the captured prey by one predator will be proportional to the number of the prey population on the boundary of the prey herd, which means that is proportional to the square root of the prey population density; it is the main reason of proposing such as functional response. This functional response has been used widely, we cite for instance the papers [6,27,29,30,32,35,36]. It follows by a several of functional responses which models this interaction by including many factors such as herd shape, predator average handling time of the prey on the bounders, we take as example the papers [3,7,9,10,19,24,26,33,38].…”

Pattern formation of a diffusive predator‐prey model with herd behavior and nonlocal prey competition

“… is the functional response, which models the interaction predator‐prey in the presence of prey herd behavior. This case of predator‐prey interaction attracts many researchers; we cite, for instance, the papers . This functional response has been followed by numerous other interaction functionals by including many other factors such as searching for the prey pack by predators, saturation of predator consumption, herd shape, so on; see, for instance, other works …”

“…cross‐)diffusion, next to other factors. In Yang, the local and the global stability of the constant positive steady state are determined where a proper Lyapunov functional is used for determining the global behavior for the positive constant steady state. In Zhu and Zhang, the existence (resp.…”

“…4,5 This functional response has been followed by numerous other interaction functionals by including many other factors such as searching for the prey pack by predators, saturation of predator consumption, herd shape, so on; see, for instance, other works. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] The impact of self-(resp. cross-)diffusion on the dynamics of predator-prey models has been always scrutinized since the pioneering work of Turing.…”

Existence and asymptotic behavior of solutions for a mathematical ecology model with herd behavior

“…For (5) with N = 1 and the additional time delay, Tang et al 11 considered the the stability of the positive equilibria and the existence of Hopf bifurcations by analyzing the corresponding characteristic equation, the normal form theory and the center manifold argument for partial functional differential equations. Recently, Yang 12 considered the steady-state bifurcations of system (4) with a = 0, both from simple and double eigenvalues.…”