last modified February 12, 2014 - 15:18 CET

Continuous-Time Dynamical Systems

Abstract

The analysis of continuous-time dynamical systems is carried out by using both brute-force and continuation methods. Main tools: AUTO2000, MATCONT, CVODE.

Examples of analyzed systems

Bifurcation diagrams of an oscillator based on hysteresis (upper and lower left panels) and state space trajectories corresponding to different parameter pairs (lower right panel). The upper panel has been obtained by using brute-force methods and associating different colours to different behaviours displayed by the system; the lower left panel shows bifurcation curves obtained by using continuation methods.

Hysteresis anim

Bifurcation diagram (left panel) and state space trajectories (right panel) of the Hindmarsh-Rose single-compartment neuron model.

HR anim

Involved People:

Major Publications:

  • Linaro D, Champneys A, Desroches M and Storace M (2012), "Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster", SIAM Journal on Applied Dynamical Systems. Vol. 11(3), pp. 939-962.
  • Linaro D, Poggi T and Storace M (2010), "Experimental bifurcation diagram of a circuit-implemented neuron model", Physics Letters A. Vol. 374, pp. 4589-4593.
  • Storace M, Linaro D and de Lange E (2008), "The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations", Chaos: An Interdisciplinary Journal of Nonlinear Science. Vol. 18(3), pp. 033128. AIP.
  • Stellardo D, Bizzarri F, Storace M and De Feo O (2007), "On the complexity of periodic and non-periodic behaviors of a hysteresis-based electronic oscillator", Chaos., Dec., 2007. Vol. 17(4), pp. 043108(1-13).
  • Bizzarri F, Stellardo D and Storace M (2006), "Bifurcation analysis and its experimental validation for a hysteresis circuit oscillator", IEEE Transactions on Circuits and Systems II: Express Briefs., July, 2006. Vol. 53(7), pp. 517-521.

Funding:

  • Italian Ministry of University and Research Grant - 2005-2007 (PRIN2005). Research network with the Universities of Milan (Polytechnic), Genoa, Naples (Second University), and Rome "La Sapienza". Title: "Design and implementation methodologies of free running and synthesised oscillators characterised by low phase noise"
  • Italian Ministry of University and Research Grant - 2003-2006 (FIRB2001). Research network with the Universities of Ferrara, Genoa, Turin, and Milan. Title: "Innovative methods for analysis and design of chaotic circuits".
  • Italian National Research Council (CNR) - 2001-2002, in the framework of the "Young researchers projects" initiative. Title: "Analysis, implementation and possible applications of an electronic oscillator based on hysteresis able to produce chaotic dynamics".

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