Bifurcation Analysis of an Impulsive Three Species Predator Prey Model

Recently, the field of research on chaotic impulsive differential equations about biological control seems to be a new increasingly interesting area, to which some scholars have paid attention. Here, we illustrate our new work about impulsive predator-prey system with Watt-type functional response. The ecosystem is of the form described in [8]:

Ay = -S2y }t =(n + l- 1)T Az = -&3z x (nT+) = x(nT) y(nT+) = y(nT) \t = nT z(nT+) = z(nT) + p with ax = x(t+)—x(t), where, x(t+) = lim x(t). ay =

y(t+)—y(t), az = z(t+)—z(t), x(t), and y(t) are functions of time representing population density of prey species, and z(t) is population size of predator species. All parameters are positive constants, hi (i = 1,2, 3) are intrinsic rates of increase or decrease, a, ft are parameters representing competitive effects between two prey, ai (i = 1,2) are coefficients of decrease of prey species due to predation, d (i = 1,2) are equal to the transformation rate of predator, 0< l <1, 0 < 6i < 1 (i = 1,2, 3), T is the period of the impulsive effects, n p N, N is the set of non-negative integers. p >0 is the bifurcation parameter.

Here, we consider the following set of parameters for our analysis: T = 6, a1 = 1, a2 = 1.1, h1 = 4.1, b2 = 4.5, b3 = 0.6, d1 = 9, d2 = 10, c = 0.5, m = 0.2, a = 0.1, ft = 0.15, S1 = 0.2, 62 = 0.15, 63 = 0.0001, l = 0.5 and the initial value (x(0), y(0), z(0)) = (3, 4, 5). Figure 9 displays the dynamic behavior of system [8] with the time series. In Figure 9, we can see, when p>pmax = 53.87 232 860, the two prey populations

10 Ways To Fight Off Cancer

10 Ways To Fight Off Cancer

Learning About 10 Ways Fight Off Cancer Can Have Amazing Benefits For Your Life The Best Tips On How To Keep This Killer At Bay Discovering that you or a loved one has cancer can be utterly terrifying. All the same, once you comprehend the causes of cancer and learn how to reverse those causes, you or your loved one may have more than a fighting chance of beating out cancer.

Get My Free Ebook

Post a comment