Akademik Veri Yönetim Sistemi
29th International Conference on Difference Equations and Applications 24-28 Jun 2024 Paris (France), Paris, Fransa, 24 - 28 Haziran 2024, ss.95
It is well known that two kinds of equations, differential and difference equations, are used in the modelling of population dynamics. When the size of the population
is rarely small or there are no overlapping generations, using difference equations is more appropriate. Moreover, it is also known that difference equations have richer
dynamical properties than continuous systems. In view of this observation, in this talk we consider a predator-prey model, and first of all, we discretize the model with
the help of piecewise constant arguments. The best advantage of this technique is that it avoids the existence of negative solutions in the discretized system. This
method creates a bridge between differential and difference systems. Then we start the investigation of the types of fixed points and analyze the flip and Neimark-Sacker
bifurcations using bifurcation theory and center manifold theorems. We also aim to construct the conditions that make our system chaotic. We support the results
obtained here with some numerical experiments.