Advances in Bio-Dynamics and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 2973

Special Issue Editor


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Guest Editor
Laboratory of Applied Maths of Le Havre, Normandie University, 76600 Le Havre, France
Interests: dynamical systems (nonlinear partial and ordinary differential equations); complex systems; applications to life sciences and neuroscience

Special Issue Information

Dear Colleagues,

We are pleased to announce a Special Issue of the journal Mathematics entitled, “Advances in Bio-Dynamics and Applications”. 

This Special Issue aims to compile research articles focusing on the qualitative analysis of dynamical systems modeling life science phenomena. From PDEs to networks and complex systems, whether deterministic or stochastic, dynamical systems offer countless possibilities to account for observed phenomena in biology. 

The goal is to provide qualitative analysis of models. This includes theoretical perspectives such as: asymptotic behavior, stability, oscillations, bifurcation, rhythms, emergent properties, synchronization, etc. Applications of interest include neuroscience, epidemiology, ecosystems, etc. However, any contribution relevant to life sciences is welcome. This includes fundamental ideas coming from physics.   

This Special Issue welcomes original research articles, short communications, and review papers that cover research that is on the forefront of advances in bio-dynamics and applications.

Dr. Benjamin Ambrosio
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dynamical systems
  • partial differential equations
  • ordinary differential equations
  • networks
  • complex systems
  • life sciences
  • neuroscience
  • epidemiology
  • ecosystems
  • bio-dynamics
  • stochastics

Published Papers (4 papers)

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Research

17 pages, 4171 KiB  
Article
Trends and Paradoxes of Competitive Evolution in the Predation Mechanism
by Evariste Sanchez-Palencia and M. A. Aziz-Alaoui
Mathematics 2024, 12(7), 1117; https://doi.org/10.3390/math12071117 - 08 Apr 2024
Viewed by 356
Abstract
We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey [...] Read more.
We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey and predators). We then develop the mathematical theory that enables us to understand the causality involved, and we identify a trend towards the emergence of the functional predation mechanism as such (and not of populations of the species involved). The realization of this trend only takes place when the conditions for it are offered by the hazards proposed to successive competitive choices. The logical structure of this trend is similar to that of the “tendency of rate of profit to fall” in certain economic models. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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26 pages, 2290 KiB  
Article
Modelling Predator–Prey Interactions: A Trade-Off between Seasonality and Wind Speed
by Dipesh Barman and Ranjit Kumar Upadhyay
Mathematics 2023, 11(23), 4863; https://doi.org/10.3390/math11234863 - 04 Dec 2023
Cited by 1 | Viewed by 703
Abstract
Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind [...] Read more.
Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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17 pages, 408 KiB  
Article
Dynamics of Optimal Cue Integration with Time-Varying Delay in the Insects’ Navigation System
by Molan Li, Da Li, Junxing Zhang, Xuanlu Xiang and Di Zhao
Mathematics 2023, 11(17), 3696; https://doi.org/10.3390/math11173696 - 28 Aug 2023
Viewed by 701
Abstract
Neural networks with a ring structure are considered biologically plausible and have the ability of enforcing unique and persistent heading representations, yielding realistic homing behaviors. Recent studies have found that insects optimally integrate sensory information from the environment for head direction by using [...] Read more.
Neural networks with a ring structure are considered biologically plausible and have the ability of enforcing unique and persistent heading representations, yielding realistic homing behaviors. Recent studies have found that insects optimally integrate sensory information from the environment for head direction by using ring attractor networks. Optimal cue integration as the basic component of a complex insect navigation system proves to consist of a ring attractor network that is coupled by some integration neurons and some uniform inhibition neurons. The dynamics of the coupled mechanisms between neurons in optimal cue integration determine whether the insects’ homing capability is affected by environmental noises. Furthermore, time delays caused by communication between different kinds of neurons may induce complex dynamical properties. These dynamical behaviors are essential for understanding the neural mechanisms of insect homing behaviors, but there is a lack of relevant research on the dynamics of optimal cue integration with time-varying delay in the insects’ navigation system. In this paper, we discuss the dynamical properties of optimal cue integration with time-varying delay and show that it is asymptotically stable and leads to a unique insect home direction. These results are critical in providing the theoretical basis for further research on insect homing behaviors and the establishment of autonomous robots that mimic insect navigation mechanisms in the future. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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18 pages, 1738 KiB  
Article
Analysis of an Integrated Pest Management Model with Impulsive Diffusion between Two Regions
by Airen Zhou
Mathematics 2023, 11(13), 2970; https://doi.org/10.3390/math11132970 - 03 Jul 2023
Viewed by 679
Abstract
This paper investigates an integrated pest management model with pulsed diffusion. As we all know, humans have been fighting against pests since they entered the age of farming. When pests are controlled, humans can achieve better harvests. We use the stroboscopic mapping of [...] Read more.
This paper investigates an integrated pest management model with pulsed diffusion. As we all know, humans have been fighting against pests since they entered the age of farming. When pests are controlled, humans can achieve better harvests. We use the stroboscopic mapping of discrete dynamic system to obtain some important lemmas. Based on the lemmas, firstly, we give the conditions for the global asymptotic stability of the periodic solution of the pest eradication boundary; secondly, the conditions for the permanence of the investigated system are derived; thirdly, numerical simulations are used to verify our obtained theoretical results; finally, increased dispersal was found to have the opposite effect on integrated pest management. We conclude that a combination of impulsive diffusion, spraying pesticides, and releasing natural enemies can play a crucial role in integrated pest management. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Synchronization in a three level Network of all-to-all quasi-periodically forced Hodgkin-Huxley Reaction-Diffusion equations
Authors: B. Ambrosio; M.A. Aziz-Alaoui; A. Oujbara
Affiliation: Normandie Univ
Abstract: This article focuses on the analysis of dynamics emerging in a Network of Hodgkin-Huxley Reaction-Diffusion equations. The network is forced with three external periodic stimulus input. A synchronization phenomenon is observed.

Title: Trends and paradoxes of the competition in the predation mechanism
Authors: Evariste Sanchez-Palencia
Affiliation: French Academy of Sciences
Abstract: This article provides a series of numerical examples of competition in the predation system showing in certain cases how the choice to increase the efficiency of the predation mechanism, (or other significant parameters) leads to the decrease of populations (both prey and predators). We then develop the mathematical theory allowing us to understand the causality and identify a trend toward the emergence of the functional mechanism of predation (and not of one or other species involved). The realization of this trend only arises under specific conditions corresponding to random specific choices. The logical structure of this trend is similar to that of the decline profit's rate in certain models of the economy.

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