| 1. |
- Aparicio, J P, et al.
(author)
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The quasi-deterministic limit of population dynamics
- 2012
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In: International Journal of Applied Mathematics and Statistics. - 0973-1377. ; 26:2, s. 30-45
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Journal article (peer-reviewed)abstract
- We review, discuss and compare different, but related, approximations to the stochastic dynamics of populations, all of them having as limit the same deterministic dynamics. The diffusion approximation, linearized diffusion approximation and the Poisson approximation are briefly revisited and their quality as approximations for large, but given, populations is addressed analytically as well as with demonstrative examples. To this end we introduce the Integer-Gauss approximation to the Poisson approach and use it to discuss the relation among different techniques.
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| 2. |
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| 3. |
- Homburg, A J, et al.
(author)
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Accumulations of T-points in a model for solitary pulses in an excitable reaction-diffusion medium
- 2005
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In: Physica D: Nonlinear Phenomena. - : Elsevier BV. - 0167-2789. ; 201:3-4, s. 212-229
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Journal article (peer-reviewed)abstract
- We consider a family of differential equations that describes traveling waves in a reaction-diffusion equation modeling oxidation of carbon oxide on a platinum surface, near the onset of spatio-temporal chaos. The organizing bifurcation for the bifurcation structure with small carbon oxide pressures, turns out to be a codimension 3 bifurcation involving a homoclinic orbit to an equilibrium undergoing a transcritical bifurcation. We show how infinitely many T-point bifurcations of multi loop heteroclinic cycles occur in the unfolding.
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| 4. |
- Mayol, C, et al.
(author)
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Class-A lasers with injected signal: Bifurcation set and Lyapunov-potential function
- 2002
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In: Physical Review A (Atomic, Molecular and Optical Physics). - 1050-2947. ; 66:1
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Journal article (peer-reviewed)abstract
- We describe the bifurcation set for a class-A laser with an external injected signal in terms of the amplitude and the frequency of the applied field. We explain the dynamical behavior of this kind of lasers in terms of a Lyapunov potential in the case where such a description is possible. In particular, a full description for the deterministic and nondeterministic dynamics can be given by using the Lyapunov potential for some of the external parameters. Depending also on the value of these parameters, the phase of the electric field drifts with time in the stochastic case.
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| 5. |
- Mayol, Catalina, et al.
(author)
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Resonance structure in a weakly detuned laser with injected signal
- 2001
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In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 11:10, s. 2587-2605
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Journal article (peer-reviewed)abstract
- We describe the qualitative dynamics and bifurcation set for a laser with injected signal for small cavity detunings. The main organizing center is the Hopf-saddle-node bifurcation from where a secondary Hopf bifurcation of a periodic orbit originates. We show that the laser's stable cw solution existing for low injections, also suffers a secondary Hopf bifurcation. The resonance structure of both tori interact, and homoclinic orbits to the "off" state are found inside each Arnold tongue. The accumulation of all the above resonances towards the Hopf-saddle-node singularity points to the occurrence of a highly degenerate global bifurcation at the codimension-2 point.
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| 6. |
- Natiello, Mario, et al.
(author)
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A Braided View of a Knotty Story
- 2013
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In: Topology and Dynamics of Chaos. - : WORLD SCIENTIFIC. - 9789814434850 - 9789814434874 ; , s. 149-168
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Book chapter (peer-reviewed)abstract
- Periodic orbits of 3-d dynamical systems admitting a Poincaré section can be described as braids. This characterisation can be transported to the Poincaré section and Poincaré map, resulting in the braid type. Information from braid types allows to estimate bounds for the topological entropy of the map while revealing detailed orbit information from the original system, such as the orbits that are necessarily present along with the given one(s) and their organisation. We review this characterisation with some examples --from a user-friendly perspective--, focusing on systems whose Poincaré section is homotopic to a disc.
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| 7. |
- Natiello, Mario A., et al.
(author)
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Modelling population dynamics based on experimental trials with genetically modified (RIDL) mosquitoes
- 2020
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In: Ecological Modelling. - : Elsevier BV. - 0304-3800. ; 424
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Journal article (peer-reviewed)abstract
- Recently, the RIDL-SIT technology has been field-tested for control of Aedes aegypti. The technique consists of releasing genetically modified mosquitoes carrying a “lethal gene”. In 2016 the World Health Organization (WHO) and the Pan-American Health Organization (PAHO) recommended to their constituent countries to test the new technologies proposed to control Aedes aegypti populations. However, issues concerning effectiveness and ecological impact have not been thoroughly studied so far. In order to study these issues, we develop an ecological model. It presents interdependent dynamics of mosquito populations and food in a homogeneous setting. Mosquito populations are described in a stochastic compartmental setup, in terms of reaction norms depending on the available food in the environment. The development of the model allows us to indicate some critical biological knowledge that is missing and could (should) be produced. Hybridisation levels, release numbers during and after intervention and population recovery time after the intervention as a function of intervention duration and target are calculated under different hypotheses with regard to the fitness of hybrids and compared with two field studies of actual interventions. This minimal model should serve as a basis for detailed models when the necessary information to construct them is produced. For the time being, the model shows that nature will not clean non-lethal introgressed genes.
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| 8. |
- Natiello, Mario, et al.
(author)
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Blowing-up of deterministic fixed points in stochastic population dynamics
- 2007
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In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 209:2, s. 319-335
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Journal article (peer-reviewed)abstract
- We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system. (C) 2007 Elsevier.Inc. All rights reserved.
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| 9. |
- Natiello, Mario, et al.
(author)
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Finns det skillnader i kvinnliga och manliga teknologers inställning till samarbetslärande i matematikundervisningen?
- 2007
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Reports (other academic/artistic)abstract
- Efter ett par terminers erfarenhets med en lättare variant av samarbetslärande inom matematikundervisningen på LTH, har försöket utvärderats via en enkät. I utvärderingen fokuserade vi på genusaspekten för att försöka ge svar till frågan om kvinnliga och manliga teknologer hade olika inställning till arbetssättet. Resultaten visar att det finns ett överlag positivt mottagande till metodiken bland alla studenter utan större skillnader mellan kvinnor och män. Examinationsresultaten tycks förbättras, om än marginellt, med den nya undervisningssättet.
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| 10. |
- Natiello, Mario, et al.
(author)
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Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes
- 2018
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In: Cogent mathematics and Statistics. - : Informa UK Limited. - 2574-2558.
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Journal article (peer-reviewed)abstract
- We develop a simulation method for Markov Jump processes with finite time steps based in a quasilinear approximation of the process and in multinomial random deviates. The second order approximation to the generating function, Error$=O(dt^{2})$, is developed in detailand an algorithm is presented. The algorithm is implemented for a Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model and compared to both the deterministic approximation and the exact simulation. Special attention is given to the problem of extinction of the infected population which is the most critical condition for the approximation.
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