Evolutionary dynamics of Lozi map have been studied and stability criteria of its fixed points are discussed in some detail. Bifurcation diagrams of this map are drawn by varying both of its parameters while assigning fixed value to other parameter. Various attractors of Lozi map appeared in diverse and interesting pattern during evolution with different pair of values of parameters and for different initial conditions. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov exponents, (LCEs), and topological entropies have been done and represented graphically. Finally, asymptotic stability method has been applied to stabilize an unstable orbit and chaotic evolution of the Lozi map has been controlled. © 2016, Jangjeon Mathematical Society. All rights reserved.