  A competitive resource-consumer dynamical model is analyzed based on an
integrated model of a competitive Lotka-Volterra model and a prey-predator
Rosenzweig-MacArthur model that we call that LV-RM model throughout this paper.
Resource growth in the absence of consumers is logistic, and competing
consumers' type II Holling's functional response made the model structure more
realistic. We used the normal form and the center manifold theorems for
bifurcation analysis of the presented model, identified Hopf and zero-Hopf
bifurcations and their directions, and discussed their biological
interpretations. We hypothesized that differentiated time scales of the
competing consumers' predatory that lead to asymmetry in competition are the
mechanisms that promote coexistence through relaxation-oscillation dynamics.
Though, other performance parameters of both competitors are the same.
Graphical representation of variations of the first Lyapunov coefficient, after
competition coefficients interplay, shows various dynamics with growing
complexity from the periodic state towards chaotic motion like R\"ossler
attractor. We presented simulations to visualize the theoretical results
obtained through bifurcation analysis.
