Human being and different species of animals having the skills to gather, transferring knowledge, processing, fine-tune and generating information throughout their lifetime. The ability of learning throughout their lifespan is referred as continuous learning which is using neurocognition mechanism. Consequently, in real world computational system of incremental learning autonomous agents also needs such continuous learning mechanism which provide retrieval of information and long-term memory consolidation. However, the main challenge in artificial intelligence is that the incremental learning of the autonomous agent when new data confronted. In such scenarios, the main concern is catastrophic forgetting(CF), i.e., while learning the sequentially, neural network underfits the old data when it confronted with new data. To tackle this CF problem many numerous studied have been proposed, however it is very difficult to compare their performance due to dissimilarity in their evaluation mechanism. Here we focus on the comparison of all algorithms which are having similar type of evaluation mechanism. Here we are comparing three types of incremental learning methods: (1) Exemplar based methods, (2) Memory based methods, and (3) Network based method. In this survey paper, methodology oriented study for catastrophic forgetting in incremental deep neural network is addressed. Furthermore, it contains the mathematical overview of impact-full methods which can be help researchers to deal with CF.