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Qualitative Analysis of a Modified Leslie-Gower Predator-prey Model with Weak Allee Effect II
Get PDFThe article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for models with (without) Allee effect and the local existence and stability of the limit cycle emerging through Hopf bifurcation has also been studied. The phase portrait diagrams are sketched to validate analytical and numerical findings
On the Lucas Difference Sequence Spaces Defined by Modulus Function
Get PDFIn this paper, firstly, we define the Lucas difference sequence spaces by the help of Lucas sequence and a sequence of modulus function. Besides, we give some inclusion relations and examine geometrical properties such as Banach-Saks type p, weak fixed point property
Environmental Balance Through Optimal Control on Pollutants
Get PDFPollution, which is a very common term has been divided as primary pollutants and secondary pollutants. Primary pollutants are those who results directly from some process whereas secondary pollutants are caused due to intermixing and reaction of primary pollutants. These pollutants result into acid rain. In this paper, a mathematical model has been developed to study the environmental impact due to acid rain. Pollutants such as primary and secondary pollutants are the causes of acid rain. Control in terms of gases emitted by factories, smog, burning of coal and fossil fuels have been applied on primary pollutants, secondary pollutants and acid rain to have an ecofriendly environment. Stability for the equilibrium points have been worked out. Simulation of the model has been carried out, which shows that there can be a clean environment if all the necessary steps are taken care of to curb this problem
A further result on the aging properties of an extended additive hazard model
Get PDFThe passing of time is an important factor for covariates in the additive and proportional hazard models. According to this idea, the extended additive hazard model (EAHM) is introduced by considering the time-varying effects of covariates and is investigated several properties of this model related to reliability analysis. In this paper, we obtain a further result for the EAHM with respect to the aging properties
Dynamics in a Respiratory Control Model With Two Delays
Get PDFIn this paper we study ventilation patterns in a set of parameter dependent nonlinear delay equations with two transport delays modeling the human respiratory control system with peripheral and central control loops. We present a convergent numerical scheme suitable to perform simulations when all disturbances and system parameters are known, then we consider the numerical identifiability of various system parameters based on ventilation data. We are especially interested in the identification of the transport delays in the control loops because these parameters are not measurable directly, but they have a strong influence on system stability/instability
Solutions of the Generalized Abel’s Integral Equation using Laguerre Orthogonal Approximation
Get PDFIn this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, together with the absolute error function. We have also carried out a numerical comparison with Chebyshev polynomials to display less error in the posed formulation
Boundedness and Square Integrability in Neutral Differential Systems of Fourth Order
Get PDFThe aim of this paper is to study the asymptotic behavior of solutions to a class of fourth-order neutral differential equations. We discuss the stability, boundedness and square integrability of solutions for the considered system. The technique of proofs involves defining an appropriate Lyapunov functional. Our results obtained in this work improve and extend some existing well-known related results in the relevant literature which were obtained for nonlinear differential equations of fourth order with a constant delay. The obtained results here are new even when our equation is specialized to the forms previously studied and include many recent results in the literature. Finally, an example is given to show the feasibility of our results
Hankel Rhotrices and Constructions of Maximum Distance Separable Rhotrices over Finite Fields
Get PDFMany block ciphers in cryptography use Maximum Distance Separable (MDS) matrices to strengthen the diffusion layer. Rhotrices are represented by coupled matrices. Therefore, use of rhotrices in the cryptographic ciphers doubled the security of the cryptosystem. We define Hankel rhotrix and further construct the maximum distance separable rhotrices over finite fields
Growth of salmonella and other foodborne pathogens on inoculated inshell pistachios during simulated delays between hulling and drying
No full textDuring harvest, pistachios are hulled, separated in water into floater and sinker streams (in large part on the basis of nut density), and then dried before storage. Higher prevalence and levels of Salmonella were previously observed in floater pistachios, but contributing factors are unclear. To examine the behavior of pathogens on hulled pistachios during simulated drying delays, floater and sinker pistachios collected from commercial processors were inoculated at 1 or 3 log CFU/g with cocktails of Salmonella and in some cases Escherichia coli O157:H7 or Listeria monocytogenes and incubated for up to 30 h at 37°C and 90% relative humidity. Populations were measured by plating onto tryptic soy agar and appropriate selective agars. In most cases, no significant growth (P \u3e 0.05) of Salmonella was observed in the first 3 h after inoculation in hulled floaters and sinkers. Growth of Salmonella was greater on floater pistachios than on corresponding sinkers and on floater pistachios with ≥25% hull adhering to the shell surface than on corresponding floaters with \u3c25% adhering hull. Maximum Salmonella populations (2 to 7 log CFU/g) were ~2-log higher on floaters than on corresponding sinkers. The growth of E. coli O157:H7 and Salmonella on hulled pistachios was similar, but a longer lag time (approximately 11 h) and significantly lower maximum populations (4 versus 5 to 6 log CFU/g; P \u3e 0.05) were predicted for L. monocytogenes. Significant growth of pathogens on hulled pistachios is possible when delays between hulling and drying are longer than 3 h, and pathogen growth is enhanced in the presence of adhering hull material. HIGHLIGHTS • Foodborne pathogens multiplied on undried inshell pistachios. • Pathogen growth was greater when hull material was present. • Drying delays of \u3e 3 h led to significant increases in pathogen populations. • Managing drying delays will reduce the risk for growth of foodborne pathogens
Growth of Salmonella on inoculated inhull pistachios during postharvest handling
No full textSalmonella has been isolated from dried pistachios in both postharvest and retail surveys. The source of Salmonella in pistachios is unknown, but introduction is possible at points during production, harvest, and postharvest activities. To examine the behavior of Salmonella on pistachios during simulated postharvest conditions, early-, mid-, and late-season inhull pistachios were collected from two commercial processors over five different harvests. Pistachios were inoculated with cocktails of nalidixic acid– or rifampin-resistant Salmonella at 0.64 to 1.59 log CFU/g (low) or 2.73 to 3.27 or 4.29 to 4.31 log CFU/g (high) and were incubated for up to 30 h under commercially relevant conditions (23, 35, or 37°C and 50 or 90% relative humidity [RH]). Populations of Salmonella were measured by plating onto tryptic soy agar and CHROMagar Salmonella with added nalidixic acid or rifampin. Individual growth curves at the same temperature and RH differed significantly among different lots of pistachios. Except for a single late-season lot in which no significant growth was observed, Salmonella multiplied under all storage conditions. In the first 3 h after inoculation, insignificant (most cases) to small (0.41 to 0.67 log CFU/g) but significant (P\u3c 0.05) mean increases in Salmonella populations were measured; the mean predicted time to achieve maximum populations (5 to 8 log CFU/g) was 16 ±4 h. In paired samples, longer lag phases, lower growth rates, and lower maximum increases were observed with inoculated inhull pistachios incubated at 238C and 50% RH compared with 35 or 37°C and 90% RH. Similar growth curves were observed at the low and high inoculum levels; throughout the 30 h of incubation, Salmonella populations were consistently ~1 to 2 log CFU/g lower on pistachios inoculated at the low inoculum level. Managing the time between harvesting and hulling will reduce the potential for growth of Salmonella on pistachios during postharvest handling