Chaotic universe model: Lotka-Volterra dynamics of the universe evolution

In this study, we consider nonlinear interactions between components such as dark energy, dark, matter and radiation in the Friedman-Robertson-Walker space-time framework and propose a simple interaction model based on time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra equation for suitable equation of state parameters. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for $0>w_{de}>-1$, $w_{dm}\ge 0$, $w_{m}\ge 0$ and $w_{r}\ge 0$ values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in time evolution of the densities. These results imply that the time evolution of the universe is chaotic in the presence of interactions between these components. The present model may has potential to solve some cosmological problems such as the singularity, cosmic coincidence, crunch, big rip, horizon, oscillations, emergence of galaxies, and large scale organization of the universe. Model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe, and offers a new perspective and a different scenario for the universe evolution unlike well known popular models.