## 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

## Oplan Termites

You Might Start Missing Your Termites After Kickin'em Out. After All, They Have Been Your Roommates For Quite A While. Enraged With How The Termites Have Eaten Up Your Antique Furniture? Can't Wait To Have Them Exterminated Completely From The Face Of The Earth? Fret Not. We Will Tell You How To Get Rid Of Them From Your House At Least. If Not From The Face The Earth.

Get My Free Ebook