Dynamic target search and tracking represents one of the most challenging problems for multi-agent systems. Effective strategies are critically needed to address numerous real-world robotic applications. Hitherto, the most common approach still relies on centrally controlled agents that become ineffective when tasked with both finding and tracking fast-moving targets in large and unstructured environments. While dynamic Particle Swarm Optimization (PSO) networks have been previously considered, the central effect played by the level of connectivity among swarming agents has been overlooked. In this paper, we present a fully decentralized swarming strategy offering a tunable exploration-exploitation multi-agent dynamics. This approach is achieved by combining adaptive interagent repulsion and an adjustable network PSO-based strategy. By tuning the topological distance between agents—ie the level of connectivity—we identify an optimal balance between exploration and exploitation leading to an effective performance of the swarm even in the presence of very fast moving targets. Beyond the quantitative results obtained through simulations, we present experimental test and validation of this approach with a fully decentralized swarm of eight ground miniature robots.