# Denis Patterson

Postdoctoral Associate

Expertise

My primary research interests relate to integral equations, dynamical systems and mathematical modeling. I am currently studying spatially extended ecological models which typically present as systems of integro-differential equations (or PDEs) on a spatial domain. I am also interested in the derivation of these equations as the limit of interacting particle systems.Profile

My research is at the intersection of dynamical systems and a number of application areas, namely ecology, neuroscience and development (how organisms grow and evolve). Tools from dynamical systems and probability theory are extremely useful in building mathematical models which can describe real-world phenomena and aid experimentalists in their investigations, as well as potentially suggesting new directions. My work involves collaboration with researchers in other disciplines to design realistic models and mathematical analysis to uncover the fine structures and predictions of these models.Courses Taught

MATH | 20a | Multi-variable Calculus |

MATH | 36a | Probability |

MATH | 37a | Differential Equations |

Scholarship

Appeby, John AD and Patterson, Denis Daniel. "Blow-up and superexponential growth in superlinear Volterra equations." __Discrete and Continuous Dynamical Systems, Series A__ 38. 8 (2019): 3993-4017.

Appleby, John AD and Patterson, Denis Daniel. "Growth Rates of Sublinear Functional and Volterra Differential Equations." __SIAM Journal on Mathematical Analysis__ 50. 2 (2019): 2086–2110.