<p>Local activity theorem is a powerful mathematical framework to predict the emergence of complexity in nonlinear dynamical systems. The application of this principle has been widely demonstrated through uncouple memristor (UM) in biological neuron. While UM provides an effective tool to model the fundamental neuron properties, the modeling is limited compared to the complexity of biological neurons. In this paper, we introduce a novel sub class of memristor termed coupling memristor (CM) from the perspective of electrical circuit theory and utilize the concept of local activity theorem to rigorously reveal the emergence of complex firing patterns in classical and extended Morris and Lecar (ML) model. This paper also provides comprehensive circuit theoretical proof that the time varying calcium activated potassium ion channel which shares the properties of calcium ion channel in biological neurons is in fact a generic CM and play a significant role in the generation of bursting dynamics in association with other nonlinear devices or UMs. This study also investigates the properties of CM through fast-slow dynamics, transformation from CM to UM, and small signal analysis. It is shown that how the fast-slow interaction gives the birth of bursting patterns, how CM can be mapped to UM with same or additional state equations and how the small-signal model may become more intricate based on the CM to UM mapped equations. It further shown that a classical ML model exhibits S-shaped DC V-I curve under the appropriate parameters modulations which in turn leads to give the birth of Saddle node homoclinic and Hopf subcritical (H_Sub) bifurcations. We further show that the insertion of an autonomous calcium activated potassium CM across the fast dynamic calcium ion channel and potassium ion channel triggers the evolution of complex dynamics which cannot be replicated by the traditional UMs in ML model. Through our comprehensive and in-depth analysis, we reveal that the mechanism to give the rise of square wave, chaotic, elliptical and parabolic bursting in complicated ML models are feasible only with the presence of calcium activated potassium CM followed by the satisfaction of local activity principle. The proposed concept further explored in the applications of Chay neuron excitable cells, Chay-Keizer pancreatic β-cell and Phantom Bursting, which provides a deeper understanding that CM in conjunction with UM can produces the biological realistic rhythms in diverse neuron models. These finding provide a basic principle to understand how neuromorphic channels functions as dynamical coupling elements and pave the way for development of new memristive devices and the design of next level of electrical circuit for the generation of diverse bursting and spikes patterns observed in nature.</p>