Manuscript Topics

In its early days, Mathematical Biology was closely linked with Dynamical Systems theory. However, apart from a few notable exceptions such as the celebrated Hodgkin-Huxley model for the action potential of the squid axon, most models could only provide qualitative descriptions of biological systems. More recently, models in Mathematical Biology have become more deeply informed by biological knowledge, as well as more data-driven, with the aim of making precise quantitative predictions and giving insight into highly specific biological questions.  
It is undoubtedly a positive development that Mathematical Biology is increasingly involved in investigating highly relevant biological questions. But as a discipline, Mathematical Biology, has become more fragmented:  
- Models are often developed on a case-by-case basis with the purpose of solving very specific and relatively isolated problems  
- The variety of modelling has expanded widely beyond the original framework primarily based on deterministic ordinary differential equations and now comprises a wide range of mathematical tools from stochastic processes to individual-based modelling.

As a consequence, Mathematical Biology has, to a certain extent, lost its ability to provide more general insights into more fundamental biological questions. In this special issue we will explore the question if Dynamical Systems can provide a unifying framework for Mathematical Biology in a similar fashion as in Theoretical Physics and if this can renew the ability of Mathematical Biology to explore the first principles of biological disciplines such as physiology, epidemiology, ecology and evolution. We invite research articles that showcase examples where Dynamical Systems have been applied in novel ways to address this challenge on topics including but not restricted to:
- novel developments in bifurcation theory
- numerical bifurcation analysis
- "equation-free" modelling of individual-based models
- data-driven mechanistic modelling
- stochastic processes, in particular, their parametrisation
- parameter identifiability

We also invite reviews that discuss the question if Dynamical Systems can serve as the common language of Mathematical Biology.

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