Dynamical systems theory for exploring regime shifts in social-ecological systems
Dynamical systems theory is well suited to studying questions regarding the dynamics and stability of social-ecological systems; indeed, it has deep and historical connections to resilience more broadly. In a dynamical systems model, quantities and processes are represented by a set of difference or differential equations; the properties of these equations can then be studied using a range of qualitative and quantitative tools. For example, stability (and loss thereof) is one key concept that can be quantified and explored using dynamical systems theory. In SES-LINK we, first, borrow from methods of systems dynamics such as causal loop diagrams to aid in the process of converting real-world systems into dynamical models. Second, to avoid the challenge of developing precise dynamical rules and specification of parameter values in a dynamical model (which is often impossible due to high uncertainty of social or ecological processes), we are exploring the use of the recently developed generalized modelling approach (see publication Lade et al. 2013). Third, although dynamical systems approaches can obscure the roles of specific actors in a system, we seek to include as far as possible human behavioural and social processes in our models, on levels from the individual (such as psychological effects) to the collective (such as governance and regulation). We use general-purpose software such as MATLAB for rapidly developing dynamical systems models, Mathematica to study their analytical properties and XPPAUT for bifurcation analysis.