ABSTRACT
The standard logistic map, one of the famous models of population growth, has found a celebrated place in the nonlinear phenomena of nature and science such as engineering, physics, chemistry and biology in the past few decades. Traditionally, the standard logistic map µx(1 − x) is controlled by a single parameter μ. In this chapter, we deal with the modulated logistic map μx p (1 − x) q , p, q > 0which is controlled by three parameters, p, q and μ. The analytical as well as graphical analysis is established to examine the complete dynamical behavior of the modulated logistic map for the parameters (p, q) = (2, 1), (1, 2) and (2, 2). Further, due to the presence of extra degree of freedom of parameters p and q, the modulated logistic map provides extended dynamical characteristics which may increase the performance of dynamical phenomena more efficiently. Furthermore, the analytical results are followed by theorems, examples, remarks, and corollaries and the graphical analysis is established by plotting period-doubling bifurcation diagrams in the prescribed range of growth rate parameter μ.
