This study explores how alternating periods of tonic and burst firing phases in neural networks contribute to memory consolidation. We develop a biophysical neural network model that leverages these brain state fluctuations to investigate the interplay between neuronal firing shifts and synaptic plasticity. The model introduces a two-stage plasticity rule, combining conventional early-phase plasticity with a novel burst-driven late-phase plasticity. Using a learning protocol where tonic firing is associated with active learning periods and burst firing is associated with rest periods, we demonstrate that burst firing resets early-phase plasticity, enabling new memory formation during subsequent tonic firing learning periods and memory consolidation through late-phase plasticity. We further confirm through a pattern recognition task that replacing burst firing with additional tonic firing or quiescent periods hinders memory consolidation. These findings suggest a mechanistic role for burst firing in memory consolidation and its importance for both computational models and experimental studies of learning.