Multidimensional formal Takens normal form

Supplementary Materials: The Bogdanov-Takens Normal Form: A Minimal Model For Single Neuron Dynamics

The Bogdanov-Takens Normal Form: A Minimal Model for Single Neuron Dynamics

Conductance-based (CB) models are a class of high dimensional dynamical systems derived from biophysical principles to describe in detail the electrical dynamics of single neurons. Despite the high dimensionality of these models, the dynamics observed for realistic parameter values is generically planar and can be minimally described by two equations. In this work, we derive the conditions to h...

Normal Forms for Coupled Takens-Bogdanov Systems

The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis for the ideal of relations and a Stanley decomposition for the ring of invariants that arise...

Computing Simplest Normal Forms for the Takens–Bogdanov Singularity

A computational method to obtain simplest normal forms, which we refer as hypernormal forms, for vector fields having a linear degeneracy corresponding to a double zero eigenvalue with geometric multiplicity one, is presented. The procedure of simplifying the classical normal forms requires some hypothesis on the nonlinear terms of the vector field. Once the hypothesis are established, differen...

Towards a Formal Framework for Multidimensional Codesign

Multidimensional codesign is a recently proposed paradigm for integrating different system dimensions in sensor networks. Examples of such dimensions are logical and physical mobility, continuous and discrete transitions, deterministic and random evolutions and features resulting from their interaction, like deterministic and stochastic hybrid behaviours. In this paper, we propose a unifying co...