This paper presents a formal framework for modelling and controlling workload dynamics in blockchain technologies. Using time-dependent transaction arrival rates and network latency distributions, we develop continuous-time differential models to describe the behaviour of blockchain systems under variable conditions. Two fundamental axioms – the Load Dynamics Axiom and the Network Response Principle – are proposed to characterise network stability and delay growth mechanisms. Optimal control strategies are formulated via Pontryagin’s Maximum Principle, enabling dynamic workload regulation in both Proof-of-Work and Proof-of-Stake networks. Furthermore, a partial differential equation model for transaction load balancing in sharded blockchain architectures is introduced. Experimental validation using numerical simulations based on realistic Ethereum network parameters demonstrates the practical applicability of the proposed models, highlighting their effectiveness in predicting and mitigating network congestion. The results demonstrate that adaptive workload control reduces transaction confirmation delays by up to 60% and maintains a stable throughput of approximately 100 transactions per second, even under highly variable load scenarios. This work contributes a novel synthesis of formal specification methods and dynamic workload management for decentralised systems, bridging theoretical insights with practical guidelines for blockchain performance optimisation. Future research directions include extending the models to Layer-2 architectures and hybrid consensus protocols.