Year 2023

• The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index

  Publication

  • L. Asselle
  • M. Izydorek
  • M. Starostka

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2023

  n this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.

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Year 2019

• Detecting coupling directions with transcript mutual information: A comparative study

  Publication

  • J. Amigó
  • B. Graff
  • G. Graff
  • R. Monetti
  • K. Tessmer

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2019

  Causal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...

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Year 2017

• Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos

  Publication

  • J. Rubin
  • J. Signerska-Rynkowska
  • J. Touboul
  • A. Vidal

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2017

  In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...

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• Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations

  Publication

  • J. Rubin
  • J. Signerska-Rynkowska
  • J. Touboul
  • A. Vidal

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2017

  This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...

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