Dynamical systems modeling

Dynamical systems modeling (DSM) is based on dynamic systems theory (DST), a mathematical theory that studies how a system evolves in time when its elements and the relationships between them are known. It uses differential or difference equations and a mathematical toolkit (e.g. analytical and numerical methods) to describe, analyse and understand general system behavior, such as the existence and stability of equilibria, including alternative stable states, thresholds, and basins of attraction. Systems, elements, and relationships are understood abstractly here, and the DSM does not focus a priori on social, ecological, or social-ecological domains of analysis, but only on the interdependencies among elements.

The link between structure and dynamics of a model leads to structural understanding that facilitates making sense of dynamical possibilities of real systems through manipulation of feedbacks, interactions between variables or initial conditions of the corresponding DSM.

Structural understanding and experimenting with models using stability and bifurcation analysis has the ability to isolate important, but potentially unexplored interactions. Stability analysis explores existence and properties of equilibria. Bifurcation analysis explores qualitative changes in system behavior caused by changes in parameter values. They are close related to equilibrium thinking and asymptotic dynamics i.e. dynamics that system achieve at some point and retain forever if it is left undisturbed.

Stochasticity, nonlinear or time-dependent processes can prevent existence of equilibria or create long transient dynamics. In such cases, reaching an equilibrium point might not be possible or relevant for ecosystems and SES management. Shifting focus from equilibrium to out-of-equilibrium thinking and transient dynamics can provide alternative explanations of phenomena that are based on endogenous processes and system structure rather than on external drivers. This, in turn, help promote adaptive and anticipatory management strategies over those that rely on control of feedbacks.

DSM allows for moving beyond case study narratives, sparse quantitative data and descriptive empirical results toward more general results and causal relationships. Used as a heuristic tool, DSM can help asking and answering what-if questions in a way that is not possible in real systems or is hardly accessible in other modeling approaches, e.g. exploring asymptotic dynamics, stability and bifurcations using agent based models (ABM) is quite limited.

An important limitation of DSM is simplification of model assumptions. This is especially visible in studying human decision making and strategic behavior because evolutionary game-theoretic models usually assume only two strategies and low agent and spatial heterogeneity. Combining modeling and empirical research methods, such as narratives and games, can help capture relevant causal relationships of the real systems and enhance understanding of emergent phenomena in SES. Complementing DSM and ABM can introduce heterogeneity of agents in the models and help explore emergent phenomena more efficiently, widen the set of answered questions and provide deeper causal understanding of SES.

Projects: PovertyTraps, BalticSES, TSL, LimnoTip, CauSES

S. Radosavljevic, T. Banitz, V. Grimm, L.-G. Johansson, E. Lindkvist, M. Schlüter, P. Ylikoski. (2023). Dynamical systems modeling for structural understanding of social-ecological systems: a primer. Ecological Complexity. Volume 56, 101052, doi.org/10.1016/j.ecocom.2023.101052

Want to know more? Email sonja.radosavljevic-@-su.se