Fractional order oxygen-plankton system under climate change

Reaction-diffusion waves in biology: new trends, recent developments

Reaction-diffusion systems are widely used in the description of propagation phenomena in biological systems, where chemical and biological processes combine to produce spatial and temporal patterns. This paper explores the recent trends and developments in the study of reaction-diffusion waves, highlighting their relevance to diverse biological contexts such as population dynamics, ecology or biomedical applications. Progress in mathematical techniques and computational methods advances our ability to model these systems, providing deeper insights into wave propagation, stability, and bifurcations. We also discuss novel models and their implications for understanding processes such as biological invasions or disease proliferation. Overall, the integration of modern theoretical frameworks with experimental data continues to push the boundaries of this interdisciplinary field, revealing new applications and mechanisms underlying biological wave dynamics.

Identification method for a fractional-order system in terms of equivalent dynamic properties

In this paper, we introduce an efficient method for identifying fractional dynamic systems using extended sparse regression and cross-validation techniques. The former identifies equations that fit the data with varying candidate functions, while the latter determines the optimal equation with the fewest terms yet ensuring accuracy. The identified optimal equation is expected to share the same dynamic properties as the original fractional system. Unlike previous studies focusing on efficiently computing fractional terms, this strategy addresses dynamic analysis from a data perspective. Importantly, in the proposed method, we treat the fractional order as a variable to account for its impact on the dynamic properties of the identified equation. This treatment enables the identified equation to successfully capture dynamic behaviors when the fractional order changes. We validate the effectiveness of the method using three classical fractional-order systems as well as an energy harvesting system. Interestingly, we find that, although the identified equations do not contain non-local terms like the original fractional-order systems, they exhibit the same stochastic P-bifurcation phenomena. In other words, we construct an equivalent equation without memory properties, sharing the dynamic properties with the original system.

Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem

Marine structure changes as a result of climate change, with potential biological implications for human societies and marine ecosystems. These changes include changes in temperatures, flow, discrimination, nutritional inputs, oxygen availability, and acidification of the ocean. In this study, a fractional-order model is constructed using the Caputo fractional operator, which singular and nol-local kernel. A model examines the effects of accelerating global warming on aquatic ecosystems while taking into account variables that change over time, such as the environment and organisms. The positively invariant area also demonstrates positive, bounded solutions of the model treated. The equilibrium states for the occurrence and extinction of fish populations are derived for a feasible solution of the system. We also used fixed-point theorems to analyze the existence and uniqueness of the model. The generalized Ulam-Hyers-Rassias function is used to analyze the stability of the system. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the power law kernel and also compared the results with an exponential law and Mittag Leffler kernel. We also produce graphs of the model at various fractional derivative orders to illustrate the important influence that the fractional order has on the different classes of the model with the memory effects of the fractional operator. To help with the oversight of fisheries, this research builds mathematical connections between the natural world and aquatic ecosystems.

Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion of various Ulam’s stability is used to guarantee the context of the stability analysis. Furthermore, the equilibrium points and the basic reproduction numbers for the proposed model are provided. The Adams type predictor-corrector algorithm has been applied for the theoretical confirmation to establish the approximate solutions. A variety of numerical plots corresponding to various fractional orders between zero and one are presented to describe the dynamical behavior of the fractional model under consideration.