Self-diffusion prerequisite is obtained as the spreading approach of biological populations. Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey–predator system. On the other side, the Allee effect among prey may cause the system to become unstable. In this paper, a diffusive prey–predator system with cooperative hunting and the weak Allee effect in prey populations is discussed. The linear stability and Hopf-bifurcation analysis had been used to examine the system’s stability. From the spatial stability of the system, the conditions for Turing instability have been derived. The multiple-scale analysis has been used to derive the amplitude equations of the system. The stability analysis of these amplitude equations leads to the formation of Turing patterns. Finally, numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D. The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impact on species distribution.

The impact of pests on crop yield is a significant worry for farmers, and finding an effective strategy to control insect population growth has become a pressing matter. This study explores the dynamic analysis of a model that incorporates natural predators to control crop pests. In the research, an analysis is conducted on the model’s positivity and boundedness, followed by an examination of the existence and stability of the equilibrium points. The study focused on analyzing bifurcations at a biologically feasible equilibrium point. The parameters considered for bifurcation are the predation rate by pests and the consumption rate of natural predators. In addition, an optimal control technique has been employed to enhance the growth of the plant population through the utilization of Pontryagin’s maximum principle. Moreover, the impact of the nine parameters on the model is examined through sensitivity analysis using the partial rank correlation coefficient method. Numerical simulations are conducted to validate the analytical findings, revealing the occurrence of bifurcation and the positive impact of control on plant population growth.

The Barrow's Holographic Dark Energy (BHDE) Model is proposed in an axially symmetric anisotropic spacetime which is employing Hubble horizon as an infrared cutoff (IR cutoff). The transition of the universe from a matter dominated era to a dark energy dominated era is investigated in this model. Furthermore, the Equation of State (EoS) parameter explains how the universe evolves with non-extensive term or Barrow parameter Delta for both phase (i) phantom era (omega(B) <=-1) and (ii) quintessence era (omega(B) >=-1). In order to reconcile the dark energy, the reconstruction of scalar field potential is considered. Some of the physical properties of the model are also described.

In this study we developed coronavirus-based medical equipment inventory model for deteriorating items under shortages of medical inventory. As the COVID-19 pandemic prevails, shortages of medical equipment occurred, and nobody with a severe effect connects hospitals and healthcare employees at some point of time. Clinical studies of the hospitalized patient have revealed that, at the beginning of COVID-19, the patient often shows symptoms related to viral pneumonia, the most common fever, sore throat, muscle pain, respiratory infections, and exhaustion. Due to rise in number of patients, there were a shortage of face masks, gloves, personal protective equipment (PPE), ventilators etc. for acutely ill patients. Supply of these products deteriorated over the time. The number of metropolises and societies affected by the coronavirus remains to grow. In this model, we have considered the important parameters like the deterioration rate is time-dependent, shortages are allowed, and the demand function is initially linear and then exponentially under a finite time horizon. Finally, model is verified with a numerical illustration and explain the sensitivity analysis. The graphs are plotted against the total cost function with respect to different parameters.

In this paper, we investigate an exact Universe which is observational viable and filled with binary mixture of perfect fluid and cosmological constant $\Lambda$. Owning the non-uniform expansion of cosmos, we have considered redshift drift $\dot{z} = -(1+z)H_{0}+H(z)$ and performed statistical test to obtain the best fit value of model parameters of derived Universe with its observed values. Here $H_{0}$ and $z$ denote the present value of Hubble constant and redshift respectively. We estimate the best fit values of Hubble constant and density parameters are $H_{0} = 68.58 \pm 0.84$ km/s/Mpc, $(\Omega_{m})_{0} = 0.26 \pm 0.010$ and $(\Omega_{\Lambda})_{0} = 0.71 \pm 0.025$ by bounding the derived model with latest observational Hubble data (OHD) while with joint Pantheon data and OHD, its values are $H_{0} = 71.93 \pm 0.58$ km/s/Mpc, $(\Omega_{m})_{0} = 0.272 \pm 0.06$ and $(\Omega_{\Lambda})_{0} = 0.74 \pm 0.09$. The analysis of deceleration parameter and jerk parameter show that the Universe in derived model is compatible with $\Lambda$CDM model.

Dispersal among species is an important factor that can govern the prey–predator model’s dynamics and cause a variety of spatial structures on a geographical scale. These structures form when passive diffusion interacts with the reaction part of the reaction–diffusion system in such a way that even if the reaction lacks symmetry-breaking capabilities, diffusion can destabilize the symmetry and allow the system to have them. In this article, we look at how dispersal affects the prey–predator model with a Hassell–Varley-type functional response when predators do not form tight groups. By considering linear stability, the temporal stability of the model and the conditions for Hopf bifurcation at feasible equilibrium are derived. We explored spatial stability in the presence of diffusion and developed the criterion for diffusion-driven instability. Using amplitude equations, we then investigated the selection of Turing patterns around the Turing bifurcation threshold. The examination of the stability of these amplitude equations led to the discovery of numerous Turing patterns. Finally, numerical simulations were performed to validate the outcomes of the analysis. The outcomes of the theoretical study and numerical simulation were accorded. Our findings demonstrate that spatial patterns are sensitive to dispersal and predator death rates.

In this paper, we investigate a scalar field cosmological model of accelerating Universe with the simplest parametrization of the equation of state parameter of the scalar field. We use H(z) data, pantheon compilation of SN Ia data and BAO data to constrain the model parameters using the χ2 minimization technique. We obtain the present values of Hubble constant H0 as 66.2−1.34+1.42, 70.7−0.31+0.32 and 67.74−1.04+1.24 for H(z), H(z) + Pantheon and H(z) + BAO respectively. In addition, we estimate the present age of the Universe in a derived model t0=14.38−0.64+0.63 for joint H(z) and pantheon compilation of SN Ia data which has only 0.88σ tension with its empirical value obtained in Plank collaboration. Moreover, the present values of the deceleration parameter q0 come out to be −0.55−0.038+0.031, −0.61−0.021+0.030 and −0.627−0.025+0.022 by bounding the Universe in the derived model with H(z), H(z) + Pantheon compilation of SN Ia and H(z) + BAO data sets, respectively. We also have performed the state-finder diagnostics to discover the nature of dark energy.

In this paper, we investigate the recently proposed New Barrow Agegraphic Dark Energy (NBADE) model by taking the distinct values of Barrow parameter delta in the context of Friedmann-Robertson-Walker (FRW) Universe. We have used different diagnostic tools to discriminate NBADE model from lambda CDM model, namely statefinder pair (r, s), (r, q), omega B - omega'(B) pair, jerk parameter and Om(z) diagnostic planes. The trajectories for the evolution of statefinder parameters r - s, r - q , omega B - omega'(B) pair, jerk parameter and O-m diagnostic are plotted of NBADE model using distinct values of the Barrow parameter delta at initially omega(B0) = 0.70 and H-0 = 67.

In a fractal world with matter (pressureless) and dark energy, we examine the recently proposed Barrow holographic dark energy model with the Granda–Oliveros IR cutoff. We depict our model Hubble parameter evolution by comparing it with the most recent cosmic chronometer data, which consists of 31 H ( z ) data points with 1 σ error bars. Also, we compare the derived model against the concordance Λ CDM model by using the dimensionless Hubble parameter E ( z ). Additionally, we show the evolution of the distance modulus μ (z) for the derived model and compare with the 580 data points of Type Ia Supernovae (Union 2.1 compilation) dataset. The consequences of the model are discussed through different cosmological parameters which describe that in the recent past, the transition of the universe’s expansion from the decelerated to an accelerated stage happened smoothly. Moreover, we demonstrate that this could be an answer for the thermal history of the universe, including the order of matter and dark energy phases. The equation of state for dark energy is also impacted by the new Barrow exponent Δ , which, depending on its value, may cause it to lie in the quintessence regime, the phantom regime, or undergo the phantom-divide crossing during evolution.

In the current study, we studied a f Q -gravitational, anisotropic, locally rotationally symmetric (LRS), Bianchi type-I spacetime universe. We have adopted the freely chosen function f Q = Q + α Q , where α is a model-free parameter. We assumed that the universe is filled with dusty string fluid and that the shear scalar ( σ ) and the expansion scalar ( θ ) are proportional to each other in order to solve field equations for the average Hubble parameter ( H ). The resultant Hubble function has been fitted with observational datasets H z and SNe Ia datasets of apparent magnitude m z in order to obtain the best fit values for the cosmological parameters. Utilizing these best fit values throughout the analysis, many cosmic phenomena are examined. We have investigated cosmographic coefficients such as H , q , j , a n d s to see if an accelerated transit phase dark energy model of the cosmos exists. Also, we have classified the dark energy models that are explored using Om diagnostic analysis; our universe model is a quintessential dark energy model. The age of the universe as it exists right now has been roughly calculated by the model.

In the current study, we studied a fQ-gravitational, anisotropic, locally rotationally symmetric (LRS), Bianchi type-I spacetime universe. We have adopted the freely chosen function fQ=Q+αQ, where α is a model-free parameter. We assumed that the universe is filled with dusty string fluid and that the shear scalar (σ) and the expansion scalar (θ) are proportional to each other in order to solve field equations for the average Hubble parameter (H). The resultant Hubble function has been fitted with observational datasets Hz and SNe Ia datasets of apparent magnitude mz in order to obtain the best fit values for the cosmological parameters. Utilizing these best fit values throughout the analysis, many cosmic phenomena are examined. We have investigated cosmographic coefficients such as H,q,j,and s to see if an accelerated transit phase dark energy model of the cosmos exists. Also, we have classified the dark energy models that are explored using Om diagnostic analysis; our universe model is a quintessential dark energy model. The age of the universe as it exists right now has been roughly calculated by the model.

Density distributions of populations with self-diffusion and interaction in a spatial domain are dynamically visualized with coupled nonlinear reaction–diffusion equations. Incorporating self-diffusion terms creates a more pragmatic modeling paradigm and provides meaningful descriptions of influences on spatiotemporal pattern formation phenomena. This paper examines the effect of self-diffusion in a food chain system with a Holling type-IV functional response and the type of spatial structures forms on a geographical scale due to the random movement of species. We discussed the existence and uniqueness of a positive equilibrium solution and obtained the Turing instability conditions for the self-diffusive food chain model. Moreover, weakly nonlinear analysis close to the Turing bifurcation boundary is used to derive the amplitude equations. The stability of the amplitude equations and sufficient conditions for the emanation of spatiotemporal patterns (such as spots, stripes, and blended patterns) are investigated. The analytical results are verified with numerical simulations. The results are applicable to all environments and can be used to understand the effects of self-diffusion in other food chain models both qualitatively and quantitatively.

This article investigates a predator-prey system in which predator species cooperate in hunting and prey species herd. We obtain a delayed predator-prey model by taking into account the fact that there is always a time delay in the conversion of biomass from prey to predator in this system. We primarily investigate the stability of positive steady state and the existence of Hopf-bifurcation in this system by using the discrete-time delay as the bifurcation parameter. The findings of this study will help us understand how realistic models of ecological systems behave in terms of dynamics.

This research study investigates Barrow holographic dark energy with an energy density of ρΛ=CH2−Δ by considering the Hubble horizon as the IR cut-off in the f(R,T) gravity framework. We employ Barrow holographic dark energy to obtain the equation of the state for the Barrow holographic energy density in a flat FLRW Universe. Concretely, we study the correspondence between quintessence, k-essence, and dilation scalar field models with the Barrow holographic dark energy in a flat f(R,T) Universe. Furthermore, we reconstruct the dynamics and potential for all these models for different values of the Barrow parameter: Δ. Via this study, we can show that for Barrow holographic quintessence, k-essence, and dilation scalar field models, if the corresponding model parameters satisfy some limitations, the accelerated expansion can be achieved.

In the current study, we developed an inventory model for the progress of any business organization. The important task of the account managers is determining an inventory optimization policy. We focus on an inventory optimization approach to support business organizations. We observe an available deteriorating items inventory model in which the demand rate is constant holding cost is time-dependent. Shortages are allowed and partially backlogged. Also validate the developed model by a numerical example and discussed the sensitivity analysis.