The properties of a time-discrete integral model of population dynamics are studied. The model equations define a dynamic system in the cone of nonnegative functions in L2. The presence of dissipator caused by spatial interaction is detected. Several bifurcations of codimensions 1 and 2 are investigated. The model may go over to chaotic behavior through a sequence of period-doubling bifurcations. The Lyapunov exponents and dimension of an attractor are found. The higher dimension of an attractor is shown to be a common feature of chaotic behavior.