Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting

Amirian, Mohammad M.; Towers, Isaac; Jovanoski, Zlatko; Irwin, Andrew J.

doi:10.1016/j.heliyon.2020.e04816

Cited by 26 publications

(18 citation statements)

References 39 publications

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“…e economic environment is a positive role, indicating the demand and contribution of the current economic development to logistics; from equation ( 16), we can find that the contribution of economic development along 6 Complexity 1978-2011 to the environmental capacity of the logistics is positive.…”

Section: Logisticsmentioning

confidence: 99%

“…e logistic differential equation has become the main tool for modeling physical, engineering, economic, and biological models [3,4] because it provides more ability in estimating the natural behavior of the model, and it also provides higher degrees of freedom [5]. In addition, the logistic equation involves memory and genetic characteristics, which are essential to describe the behavior of the ecological model [6]. On the other hand, the logistic model can demonstrate the interaction relationship between two species since the earliest model was published by Verhulst [7] in 1838.…”

Section: Introductionmentioning

confidence: 99%

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An Analytical Study of the External Environment of the Coevolution between Manufacturing and Logistics Based on the Logistic Model

Zhou

2021

Complexity

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This paper focuses on the external environmental capacity of the coevolution system of the manufacturing industry and logistics industry. This paper first constructs a dynamic model of the external environmental capacity of the coevolution system by using the logistic model and then simulates the effects of two factors: one factor is the institutional environment affected by the random interference factors of policy and the other factor is the industrial environment affected by the random interference factors of the industrial economy on the coevolution system. This paper discusses the cooperative mechanism of external random interference factors on system evolution, analyzes the nonlinear variation of external environmental factors with time, and gives the estimation method. Finally, we provide an example to prove our findings.

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Section: Logisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Analytical Study of the External Environment of the Coevolution between Manufacturing and Logistics Based on the Logistic Model

Zhou

2021

Complexity

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“…This mathematical tool provides a principled framework for incorporating memory effects into ODE systems (see e.g. [32,33,39,40]), thus allowing a systematic analysis and quantification of memory effects in commonly used dynamical models of ecological communities. The mutual interaction model describes the dynamics of species abundances X i , which depends on the growth rates b i , death rates k i , and inhibition functions f i , where K ij and n denote interaction constants and Hill coefficients, respectively [18].…”

Section: Modelmentioning

confidence: 99%

Quantifying the impact of ecological memory on the dynamics of interacting communities

Khalighi

Gonze

Faust

et al. 2021

Preprint

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Ecological memory refers to the influence of past events on the response of an ecosystem to exogenous or endogenous changes. Memory has been widely recognized as a key contributor to the dynamics of ecosystems and other complex systems, yet quantitative community models often ignore memory and its implications. Recent studies have shown how interactions between community members can lead to the emergence of resilience and multistability under environmental perturbations. We demonstrate how memory can complement such models. We use the framework of fractional calculus to study how the outcomes of a well-characterized interaction model are affected by gradual increases in ecological memory under varying initial conditions, perturbations, and stochasticity. Our results highlight the implications of memory on several key aspects of community dynamics. In general, memory slows down the overall dynamics and recovery times after perturbation, thus reducing the system's resilience. However, it simultaneously mitigates hysteresis and enhances the system's capacity to resist state shifts. Memory promotes long transient dynamics, such as long-standing oscillations and delayed regime shifts, and contributes to the emergence and persistence of alternative stable states. Collectively, these results highlight the fundamental role of memory on ecological communities and provide new quantitative tools to analyse its impact under varying conditions.

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“…In Ahmed et al [28] have introduced the fractional-order LV system. Recent studies have generalized LV models to two-predator one-prey dynamics [29] and analysed a LV fractional-order model using the Caputo fractional derivative [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators

et al. 2021

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In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.

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Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting

Cited by 26 publications

References 39 publications

An Analytical Study of the External Environment of the Coevolution between Manufacturing and Logistics Based on the Logistic Model

An Analytical Study of the External Environment of the Coevolution between Manufacturing and Logistics Based on the Logistic Model

Quantifying the impact of ecological memory on the dynamics of interacting communities

Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators

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