ZnO based nanoparticles find a wide range of applications starting from biosensors and drug-delivery systems to solar cells. Keeping an eye on the prospect for an application in the field of biotechnology, we analyze Cu-doped ZnO nanoparticles after the fabrication and necessary characterization of the XRD data obtained, by using the tools of Nonlinear Dynamical Theory (NLD). One of the tools used called Lyapunov Exponent, bears the signature of the dynamical evolution of the particles as well as structure formation. This is calculated in order to quantify the underlying strange attractor present in the nanosystems, which happens to be the driving force behind the structure formation. The changes in the values of this parameter with the variation of the physical and chemical conditions, would pave the way for an efficient calibration for meaningful biological applications, which happens to be the focus of the present work. Differently sized ZnO nano particles are obtained by changing dopant percentage for inhibiting human pathogenic bacteria. Calibrations are made between the Zone of Inhibition (ZOI) and Lyapunov Exponent to obtain the required dopant percentage for a given ZOI vis-à-vis the same anti-bacterial effectiveness in terms of ZOI of a ZnO doped nano particle. Copyright © 2016 VBRI Press.