ORCID Profile
0000-0002-5890-0971
Current Organisation
Universidade Nova de Lisboa
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Publisher: Springer Science and Business Media LLC
Date: 17-06-2016
Publisher: Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
Date: 2021
DOI: 10.34619/E4VD-P551
Publisher: IOP Publishing
Date: 26-03-2009
Publisher: World Scientific Pub Co Pte Lt
Date: 09-2016
DOI: 10.1142/S0218127416501674
Abstract: In this paper, we investigate the dynamics of a [Formula: see text] operon model with delayed feedback and diffusion effect. If the system is without delay or the delay is small, the positive equilibrium is stable so that there are no spatial patterns formed while the time delay is large enough the equilibrium becomes unstable so that rich spatiotemporal dynamics may occur. We have found that time delay can not only incur temporal oscillations but also induce imbalance in space. With different initial values, the system may have different spatial patterns, for instance, spirals with one head, four heads, nine heads, and even microspirals.
Publisher: Springer Science and Business Media LLC
Date: 29-05-2009
Publisher: Hindawi Limited
Date: 2015
DOI: 10.1155/2015/343528
Publisher: Elsevier BV
Date: 09-2014
Publisher: Elsevier BV
Date: 11-2012
Publisher: Elsevier BV
Date: 04-2016
Publisher: World Scientific Pub Co Pte Lt
Date: 04-2015
DOI: 10.1142/S0218127415500583
Abstract: In this paper, we investigate the codimension-two double Hopf bifurcation in delay-coupled van der Pol–Duffing oscillators. By using normal form theory of delay differential equations, the normal form associated with the codimension-two double Hopf bifurcation is calculated. Choosing appropriate values of the coupling strength and the delay can result in nonresonance and weak resonance double Hopf bifurcations. The dynamical classification near these bifurcation points can be explicitly determined by the corresponding normal form. Periodic, quasi-periodic solutions and torus are found near the bifurcation point. The numerical simulations are employed to support the theoretical results.
Publisher: AIP Publishing
Date: 20-04-2011
DOI: 10.1063/1.3578046
Abstract: In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the d ing terms. Hopf bifurcations and litude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.
Publisher: AIP Publishing
Date: 14-11-2008
DOI: 10.1063/1.3013195
Abstract: We investigate the dynamics of a d ed harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov–Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
Publisher: Elsevier BV
Date: 10-2009
No related grants have been discovered for Jose Paulo Santos.