Blockchain networks have attracted tremendous attention for creating cryptocurrencies and decentralized economies built on peer-to-peer protocols. However, the complex nature of the dynamics and feedback mechanisms within these economic networks has rendered it difficult to reason about the growth and evolution of these networks. Hence, proper mathematical frameworks to model and analyze the behavior of blockchain-enabled networks are essential. To address this need, we establish a formal mathematical framework, based on dynamical systems, to model the core concepts in blockchain-enabled economies. Drawing on concepts from differential games, control engineering, and stochastic dynamical systems, this paper proposes a methodology to model, simulate, and engineer networked token economies. To illustrate our framework, a model of a generalized token economy is developed, where miners provide a commodity service to a platform in exchange for a cryptocurrency and users consume a service from the platform. We illustrate the dynamics of token economies by simulating and testing two different block reward strategies. We then conclude by outlining future research directions that will integrate additional methods from signal processing and control theory into the toolkit for designers of blockchain-enabled economic systems.