Agent-based models represent the interaction between a multiplicity of agents through dynamic systems, often giving rise to intricate and complex dynamics. We can extend this type of economic analysis by emphasizing that economic agents have memories, form expectations, and are guided by intentional behavior within the context of a certain decision horizon. However, it is important to note that the agents' decisions and actions change the economic environment and affect the system dynamics. The interaction of agents is often stylized as predator-prey, competitive and cooperative interactions in the context of Lotka-Volterra systems. We start with these types of systems and show that economic agents' decisions can be understood as a perturbation term in the general system dynamics. The dynamics of a model with zero time-horizon, which has small effects on the system dynamics, can often be studied analytically and taken as starting point for a numerical analysis with a longer time horizon. Since, due to nonlinearities, multiple equilibria frequently arise, this generates path dependency and complex dynamics. We solve these types of models by using dynamic programming with a flexible grid size that can capture multiple equilibria and threshold and bifurcation behavior. Heterogeneity of agents and multiple attractors predict a bimodal distribution of outcomes which can empirically be verified using Markov transition matrices. We give a number of examples from resource economics, development economics, investment theory, industrial organization, imperfect capital markets, growth, distribution, and climate change. We give prototype examples and illustrate economic mechanisms wherein such complicated dynamics, e.g., those with threshold and bifurcation behavior, can occur. These types of models can not only be empirically tested, but have strong policy implications in the sense that policy can tilt the dynamics toward superior equilibria and increase the domain of attraction for preferable equilibria.