Mathematical and Computational Applications

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9 pages, 859 KiB

Open AccessFeature PaperArticle

Influence of a Modulated Parameter on Hantavirus Infection

by María Susana Torre, Anais Acquaviva, Jean-Marc Boyer and Jorge Tredicce

Math. Comput. Appl. 2019, 24(3), 68; https://doi.org/10.3390/mca24030068 - 10 Jul 2019

Viewed by 2659

We study the dynamical behavior of a model commonly used to describe the infection of mice due to hantavirus (and, therefore, its possibility of propagation into human populations) when a parameter is changed in time. In particular, we study the situation when the [...] Read more.

We study the dynamical behavior of a model commonly used to describe the infection of mice due to hantavirus (and, therefore, its possibility of propagation into human populations) when a parameter is changed in time. In particular, we study the situation when the ecological conditions (e.g., climate benignity, food availability, and so on) change periodically in time. We show that the density of infected mice increases abruptly as the parameter crosses a critical value. We correlate such a situation with the observed sudden outbreaks of hantavirus. Finally, we discuss the possibility of preventing a hantavirus epidemic. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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9 pages, 634 KiB

Open AccessArticle

Exact Evaluation of Statistical Moments in Superradiant Emission

by Gilberto M. Nakamura, Brenno Cabella and Alexandre S. Martinez

Math. Comput. Appl. 2019, 24(2), 66; https://doi.org/10.3390/mca24020066 - 23 Jun 2019

Viewed by 2916

Abstract

Superradiance describes the coherent collective radiation caused by the interaction between many emitters, mediated by a shared electromagnetic field. Recent experiments involving Bose–Einstein condensates coupled to high-finesse cavities and interacting quantum dots in condensed-matter have attracted attention to the superradiant regime as a [...] Read more.

Superradiance describes the coherent collective radiation caused by the interaction between many emitters, mediated by a shared electromagnetic field. Recent experiments involving Bose–Einstein condensates coupled to high-finesse cavities and interacting quantum dots in condensed-matter have attracted attention to the superradiant regime as a fundamental step to create quantum technologies. Here, we consider a simplified description of superradiance that allows the evaluation of statistical moments. A correspondence with the classical birthday problem recovers the statistical moments for discrete time and an arbitrary number of emitters. In addition, the correspondence provides a way to calculate the degeneracy of the problem. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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14 pages, 783 KiB

Open AccessArticle

Functional Ca²⁺ Channels between Channel Clusters are Necessary for the Propagation of IP₃R-Mediated Ca²⁺ Waves

by Estefanía Piegari and Silvina Ponce Dawson

Math. Comput. Appl. 2019, 24(2), 61; https://doi.org/10.3390/mca24020061 - 11 Jun 2019

Cited by 1 | Viewed by 2520

Abstract

The specificity and universality of intracellular Ca

^{2 +}

signals rely on the variety of spatio-temporal patterns that the Ca

^{2 +}

concentration can display. Ca

^{2 +}

release into the cytosol through inositol 1,4,5-trisphosphate receptors (IP

_{3}

Rs) is key for this [...] Read more.

The specificity and universality of intracellular Ca

^{2 +}

signals rely on the variety of spatio-temporal patterns that the Ca

^{2 +}

concentration can display. Ca

^{2 +}

release into the cytosol through inositol 1,4,5-trisphosphate receptors (IP

_{3}

Rs) is key for this variety. The opening probability of IP

_{3}

Rs depends on the cytosolic Ca

^{2 +}

concentration. All of the dynamics are then well described by an excitable system in which the signal propagation depends on the ability of the Ca

^{2 +}

released through one IP

_{3}

R to induce the opening of other IP

_{3}

Rs. In most cell types, IP

_{3}

Rs are organized in clusters, i.e., the cytosol is a “patchy” excitable system in which the signals can remain localized (i.e., involving the release through one or more IP

_{3}

Rs in a cluster), or become global depending on the efficiency of the Ca

^{2 +}

-mediated coupling between clusters. The spatial range over which the signals propagate determines the responses that the cell eventually produces. This points to the importance of understanding the mechanisms that make the propagation possible. Our previous qualitative comparison between experiments and numerical simulations seemed to indicate that Ca

^{2 +}

release not only occurs within the close vicinity of the clearly identifiable release sites (IP

_{3}

R clusters) but that there are also functional IP

_{3}

Rs in between them. In this paper, we present a quantitative comparison between experiments and models that corroborate this preliminary conclusion. This result has implications on how the Ca

^{2 +}

-mediated coupling between clusters works and how it can eventually be disrupted by the different Ca

^{2 +}

trapping mechanisms. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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16 pages, 2553 KiB

Open AccessFeature PaperArticle

Structures and Instabilities in Reaction Fronts Separating Fluids of Different Densities

by Johan Llamoza and Desiderio A. Vasquez

Math. Comput. Appl. 2019, 24(2), 51; https://doi.org/10.3390/mca24020051 - 17 May 2019

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Abstract

Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts [...] Read more.

Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts with diffusive instabilities. We focus in fluids confined in Hele–Shaw cells or porous media, with the hydrodynamics modeled by Brinkman’s equation. The time evolution of the front is described with a Kuramoto–Sivashinsky (KS) equation coupled to the fluid velocity. A linear stability analysis shows a transition to convection that depends on the density differences between reacted and unreacted fluids. A stabilizing density gradient can surpress the effects of diffusive instabilities. The two-dimensional numerical solutions of the nonlinear equations show an increase of speed due to convection. Brinkman’s equation lead to the same results as Darcy’s laws for narrow gap Hele–Shaw cells. For large gaps, modeling the hydrodynamics using Stokes’ flow lead to the same results. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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16 pages, 4616 KiB

Open AccessArticle

Time Recurrence Analysis of a Near Singular Billiard

by Rodrigo Simile Baroni, Ricardo Egydio de Carvalho, Bruno Castaldi and Bruno Furlanetto

Math. Comput. Appl. 2019, 24(2), 50; https://doi.org/10.3390/mca24020050 - 8 May 2019

Cited by 1 | Viewed by 3286

Abstract

Billiards exhibit rich dynamical behavior, typical of Hamiltonian systems. In the present study, we investigate the classical dynamics of particles in the eccentric annular billiard, which has a mixed phase space, in the limit that the scatterer is point-like. We call this configuration [...] Read more.

Billiards exhibit rich dynamical behavior, typical of Hamiltonian systems. In the present study, we investigate the classical dynamics of particles in the eccentric annular billiard, which has a mixed phase space, in the limit that the scatterer is point-like. We call this configuration the near singular, in which a single initial condition (IC) densely fills the phase space with straight lines. To characterize the orbits, two techniques were applied: (i) Finite-time Lyapunov exponent (FTLE) and (ii) time recurrence. The largest Lyapunov exponent λ was calculated using the FTLE method, which for conservative systems, λ > 0 indicates chaotic behavior and λ = 0 indicates regularity. The recurrence of orbits in the phase space was investigated through recurrence plots. Chaotic orbits show many different return times and, according to Slater’s theorem, quasi-periodic orbits have at most three different return times, the bigger one being the sum of the other two. We show that during the transition to the near singular limit, a typical orbit in the billiard exhibits a sharp drop in the value of λ, suggesting some change in the dynamical behavior of the system. Many different recurrence times are observed in the near singular limit, also indicating that the orbit is chaotic. The patterns in the recurrence plot reveal that this chaotic orbit is composed of quasi-periodic segments. We also conclude that reducing the magnitude of the nonlinear part of the system did not prevent chaotic behavior. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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7 pages, 615 KiB

Open AccessFeature PaperArticle

Inadequate Sampling Rates Can Undermine the Reliability of Ecological Interaction Estimation

by Brenno Cabella, Fernando Meloni and Alexandre S. Martinez

Math. Comput. Appl. 2019, 24(2), 48; https://doi.org/10.3390/mca24020048 - 30 Apr 2019

Cited by 4 | Viewed by 4076

Abstract

Cycles in population dynamics are abundant in nature and are understood as emerging from the interaction among coupled species. When sampling is conducted at a slow rate compared to the population cycle period (aliasing effect), one is prone to misinterpretations. However, aliasing has [...] Read more.

Cycles in population dynamics are abundant in nature and are understood as emerging from the interaction among coupled species. When sampling is conducted at a slow rate compared to the population cycle period (aliasing effect), one is prone to misinterpretations. However, aliasing has been poorly addressed in coupled population dynamics. To illustrate the aliasing effect, the Lotka–Volterra model oscillatory regime is numerically sampled, creating prey–predator cycles. We show that inadequate sampling rates may produce inversions in the cause-effect relationship among other artifacts. More generally, slow acquisition rates may distort data interpretation and produce deceptive patterns and eventually leading to misinterpretations, as predators becoming preys. Experiments in coupled population dynamics should be designed that address the eventual aliasing effect. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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12 pages, 6084 KiB

Open AccessArticle

Suppression of Phase Synchronization in Scale-Free Neural Networks Using External Pulsed Current Protocols

by Bruno Rafael Reichert Boaretto, Roberto C. Budzinski, Thiago L. Prado and Sergio Roberto Lopes

Math. Comput. Appl. 2019, 24(2), 46; https://doi.org/10.3390/mca24020046 - 24 Apr 2019

Cited by 3 | Viewed by 3241

Abstract

The synchronization of neurons is fundamental for the functioning of the brain since its lack or excess may be related to neurological disorders, such as autism, Parkinson’s and neuropathies such as epilepsy. In this way, the study of synchronization, as well as its [...] Read more.

The synchronization of neurons is fundamental for the functioning of the brain since its lack or excess may be related to neurological disorders, such as autism, Parkinson’s and neuropathies such as epilepsy. In this way, the study of synchronization, as well as its suppression in coupled neurons systems, consists of an important multidisciplinary research field where there are still questions to be answered. Here, through mathematical modeling and numerical approach, we simulated a neural network composed of 5000 bursting neurons in a scale-free connection scheme where non-trivial synchronization phenomenon is observed. We proposed two different protocols to the suppression of phase synchronization, which is related to deep brain stimulation and delayed feedback control. Through an optimization process, it is possible to suppression the abnormal synchronization in the neural network. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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17 pages, 564 KiB

Open AccessArticle

Finite Symmetries in Agent-Based Epidemic Models

by Gilberto M. Nakamura, Ana Carolina P. Monteiro, George C. Cardoso and Alexandre S. Martinez

Math. Comput. Appl. 2019, 24(2), 44; https://doi.org/10.3390/mca24020044 - 23 Apr 2019

Cited by 4 | Viewed by 3402

Abstract

Predictive analysis of epidemics often depends on the initial conditions of the outbreak, the structure of the afflicted population, and population size. However, disease outbreaks are subjected to fluctuations that may shape the spreading process. Agent-based epidemic models mitigate the issue by using [...] Read more.

Predictive analysis of epidemics often depends on the initial conditions of the outbreak, the structure of the afflicted population, and population size. However, disease outbreaks are subjected to fluctuations that may shape the spreading process. Agent-based epidemic models mitigate the issue by using a transition matrix which replicates stochastic effects observed in real epidemics. They have met considerable numerical success to simulate small scale epidemics. The problem grows exponentially with population size, reducing the usability of agent-based models for large scale epidemics. Here, we present an algorithm that explores permutation symmetries to enhance the computational performance of agent-based epidemic models. Our findings bound the stochastic process to a single eigenvalue sector, scaling down the dimension of the transition matrix to

o (N^{2})

. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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16 pages, 6045 KiB

Open AccessArticle

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

by Roberto C. Budzinski, Bruno Rafael Reichert Boaretto, Thiago L. Prado and Sergio Roberto Lopes

Math. Comput. Appl. 2019, 24(2), 42; https://doi.org/10.3390/mca24020042 - 20 Apr 2019

Cited by 3 | Viewed by 3144

Abstract

The study of synchronization in complex networks is useful for understanding a variety of systems, including neural systems. However, the properties of the transition to synchronization are still not well known. In this work, we analyze the details of the transition to synchronization [...] Read more.

The study of synchronization in complex networks is useful for understanding a variety of systems, including neural systems. However, the properties of the transition to synchronization are still not well known. In this work, we analyze the details of the transition to synchronization in complex networks composed of bursting oscillators under small-world and scale-free topologies using recurrence quantification analysis, specifically the determinism. We demonstrate the existence of non-stationarity states in the transition region. In the small-world network, the transition region denounces the existence of two-state intermittency. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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13 pages, 3196 KiB

Open AccessArticle

Observable for a Large System of Globally Coupled Excitable Units

by Santiago Boari, Gonzalo Uribarri, Ana Amador and Gabriel B. Mindlin

Math. Comput. Appl. 2019, 24(2), 37; https://doi.org/10.3390/mca24020037 - 6 Apr 2019

Cited by 4 | Viewed by 3653

Abstract

The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce [...] Read more.

The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim. Full article

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)

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