Asymptotic Behavior of Impulsive Differential Equations

González, Patricio Aroca; Pinto, Manuel

doi:10.1216/rmjm/1181072108

Cited by 7 publications

(3 citation statements)

References 6 publications

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“…Additionally, we modeled the seasonal births through a succession of discrete times, which generates a discontinuity in the abundance curves, differentiating the demographic patterns of each species. This system of differential equations is known as an impulsive system and provides a theoretical framework that captures this phenomenon (Samoilenko and Perestyuk 1995;González and Pinto 1996;Hakl et al 2017;Pinto et al 2018;Castillo et al 2019;Lu et al 2022) 12where, the variation discrete is defined with . Products , and…”

Section: Model Formulationmentioning

confidence: 99%

Body size modulates demographic patterns of top predators and their native and invasive prey: A biomathematical approach

Campillay-Llanos,

Pinto,

Osorio

2024

Ecol Austral

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The arrival of invasive species in native communities impacts the structure and functioning of ecosystems, and is considered a critical indicator of loss of biodiversity. Exploring the effects of new species in communities presents challenges addressable through theoretical ecology. Species body size not only shapes trophic relationships, but may also impact predator success and facilitate species coexistence. However, little attention has been paid to the effects of differences in species body size on interactions between native and invasive primary consumers, which could be relevant to their coexistence with higher-level predators. Our aim is to investigate demographic patterns using a dynamic, mechanistic model of two age-structured primary consumers (one invasive and one native) sharing a plant resource and preyed upon by a common predator. In our model, we highlight three crucial phenomena: the structuring of primary consumers into adults and juveniles, reproduction occurring in discrete pulses, and the seasonal addition of new individuals to the population. Hence, the success of one species over the other relies on its reproductive capacity to incorporate individuals in each reproductive cycle. Our simulations reveal that abundance patterns are influenced by body size, suggesting that changes in predator body size could serve as key indicators of shifts in community structure.

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Section: Model Formulationmentioning

confidence: 99%

Body size modulates demographic patterns of top predators and their native and invasive prey: A biomathematical approach

Campillay-Llanos,

Pinto,

Osorio

2024

Ecol Austral

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“…Many researchers have studied the qualitative properties like existence, uniqueness, and asymptotic behaviour of impulsive differential equations using various techniques. These studies are found in the articles cited [1,2,15,26,35,37] and reference their in.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of classical and mild solutions of fractional Cauchy problem with impulses

2023

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In this manuscript, we have established conditions for the existence and uniqueness of mild and classical solutions to the fractional order Cauchy problem by including and without including impulses over the completed norm linear space (Banach space). Conditions are established using the concept of generators and the generalised Banach fixed point theorem, which are weaker conditions than the previously derived conditions. We have also established the conditions under which a mild solution to the problem gives rise to a classical solution to the given problem. Finally, illustrations of the existence and uniqueness of the solution are provided to validate our derived results.

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“…The techniques used in the proof are based on an inequality of Gronwall -Bellman type and succesive aproximations. The method used is analogous to those of [3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%