Chaos analysis for the Lotka-Volterra type coupled equations

In this thesis, chaos analysis was performed in Lotka-Volterra type correlative equations. Within the scope of the thesis, two different Lotka-Volterra models are discussed. The first one is the four-dimensional correlated Lotka-Volterra equation and the other is the correlated equation system developed to model cancer spread. Both equation systems were solved numerically with the help of Matlab, and stability analyzes were performed by obtaining stable points of the equations. In addition, both model systems are solved separately and their time dependent dynamics are examined, the results are shown in phase spaces and it is shown that both model systems will produce chaotic dynamics for different initial conditions. Lyapunav exponents were calculated by obtaining chaotic attractors using chaos analysis methods. While chaotic dynamics is not observed in low-dimensional Lotka-Volterra equations, in this thesis, we have shown that chaotic dynamics will occur in both the high-dimensional Lotka-Voplterra correlated equation system and the correlated equation system used to model cancer spread. Both studies are based on a more detailed and advanced analysis of the model systems available in the literature. Keywords: Lotka-Volterra model, Chaos, Strange attractor, Lorenz attractor, Stability analysis, Fixed points, Canser dynamics, Lyapunov exponen