Pulsating solitons are intriguing objects in laser physics and nonlinear science. Recently, emerging works on the pulsating multi-solitons have raised interest in interactions and synchronizations within multiple breathers. However, with their separation of the order of nanoseconds, the evolution and underlying dynamics of multiple pulsating solitons remain uncharted. In this work, we bring initial insights into the pulsating dual-soliton (PDS) with a separation of three orders of magnitude of the pulse duration. Chaotic, synchronous, and asynchronous pulsations are revealed to be controlled by the pump power. Specifically, two solitons can pulsate synchronously in the form of a frozen limit cycle. The asynchronous PDS at a high pump power brings the rotating limit cycle in the phase space. Unveiling the evolutionary dynamics of PDS, this work has potential in all-optical storage, signal encoding, and time division multiplexing communications.