Despite remarkable capabilities, Large language models (LLMs) struggle with incrementally updating knowledge without catastrophic forgetting or indiscriminate learning. In contrast, humans effortlessly integrate new information, detect conflicts with existing beliefs, and selectively update their knowledge. This work introduces a novel paradigm inspired by human brain: Cognitive Aware Incremental Knowledge Update. We implement and evaluate two key components within existing LLM architectures: (1) Inner State Awareness, allowing LLMs to classify new information as novel, familiar, or conflicting; and (2) targeted updates through Differentiated Plasticity, distinguishing between neurons containing previous knowledge (busy) and rarely used neurons (free). Through a series of controlled experiments, we demonstrate the potential benefits of this approach, including improved preservation of prior knowledge during updates, more effective handling of conflicting information, and enhanced ability to target specific knowledge for updates.