Applying exponential unit for breaking symmetry of memristive maps

The emergence of memristors has piqued significant interest in memristive maps due to their unique characteristics. In this paper, we introduce a novel and effective method for constructing memristor maps, leveraging the power of exponential units. Interestingly, the incorporation of these exponential units disrupts symmetry and alters the count of fixed points within the map. The method is simple to build maps with chaos and higher order maps. These make our work different from existing methods. To demonstrate the efficacy of our approach, we have focused our attention on examining the dynamics, feasibility, and practical applications of a specific map, referred to as the EPMM₁ map. Furthermore, we show that by extending this approach, it becomes straightforward to create other innovative memristive maps, including those with multiple memristors.