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Abstract This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto’s approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

This paper presents novel criteria for investigating the oscillatory behavior of even-order neutral differential equations. By employing a comparative approach, we established the oscillation properties of the studied equation through comparisons with well-understood first-order equations with known oscillatory behavior. The findings of this study introduce fresh perspectives and enrich the existing body of oscillation criteria found in the literature. To illustrate the practical application of our results, we provide an illustrative example.

The purpose of this study is to develop new iterative oscillation criteria for second-order half-linear advanced dynamic equations. These findings improve and extend recently established criteria for the same equation by several authors as well as encompass the existing classical criteria for associated ordinary dynamic equations. Some examples are given to show that the outcomes are accurate, practical, and adaptable.

This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function class to obtain new criteria of the Kamenev type, which guarantees that all nonoscillatory solutions converge to zero. This approach is characterized by the possibility of applying its conditions to a wider area of equations. This is not the only aspect that distinguishes our results; we also use improved relationships between the solution and the corresponding function, which in turn is reflected in a direct improvement of the criteria. The findings in this article extend and generalize previous findings in the literature and also improve some of these findings.

This paper investigates the asymptotic and oscillatory properties of a distinctive class of third-order linear differential equations characterized by multiple delays in a noncanonical case. Employing the comparative method and the Riccati method, we introduce the novel and rigorous criteria to discern whether the solutions of the examined equation exhibit oscillatory behavior or tend toward zero. Our study contributes to the existing literature by presenting theories that extend and refine the understanding of these properties in the specified context. To validate our findings and demonstrate their applicability in a general setting, we offer two illustrative examples, affirming the robustness and validity of our proposed criteria.

This study introduces a newly modified Lorenz model capable of demonstrating bifurcation within a specified range of parameters. The model demonstrates various bifurcation behaviors, which are depicted as distinct structures in the diagram. The study aims to discover and analyze the existence and stability of fixed points in the model. To achieve this, the center manifold theorem and bifurcation theory are employed to identify the requirements for pitchfork bifurcation, period-doubling bifurcation, and Neimark–Sacker bifurcation. In addition to theoretical findings, numerical simulations, including bifurcation diagrams, phase pictures, and maximum Lyapunov exponents, showcase the nuanced, complex, and diverse dynamics. Finally, the study applies the Ott–Grebogi–Yorke (OGY) method to control the chaos observed in the reduced modified Lorenz model.

Rehab H Ashour,1,2 Eman A Abdelkader,3 Omar Hamdy,4 Mohamed Elmetwally,4 Wafaa Laimon,5 Mohamed A Abd-Elaziz1 1Clinical Pharmacology Department, Faculty of Medicine, Mansoura University, Mansoura, Egypt; 2Pharmacology & Toxicology Department, Faculty of Medicine at Al-Qunfudah, Umm Al-Qura University, Al-Qunfudah, Kingdom of Saudi Arabia; 3Internal Medicine Department, Faculty of Medicine, Mansoura University, Specialized Medical Hospital, Mansoura, Egypt; 4Surgical Oncology Department, Faculty of Medicine, Oncology Center Mansoura University “OCMU”, Mansoura, Egypt; 5Pediatric Endocrinology and Diabetes Unit, Department of Pediatrics, Faculty of Medicine, Mansoura University, Mansoura University Children’s Hospital, Mansoura, EgyptCorrespondence: Rehab H Ashour, Clinical Pharmacology Department, Faculty of Medicine, Mansoura University, 60 El-Gomhoria Street, Mansoura, Al-Dakahlia, 35516, Egypt, Tel +2 01005409956, Fax +20 50 2248203, Email drrehab40@mans.edu.eg; rhashour@uqu.edu.saBackground: The misuse of antimicrobials has major consequences, particularly antimicrobial resistance (AMR) and antimicrobials’ related adverse effects. So, the WHO proposed antimicrobial surveillance to improve antimicrobials use. This point prevalence survey (PPS) was conducted to illustrate the prevalence of antimicrobial use at Mansoura University hospitals (MUH), Egypt.Methods: The survey process used was adapted from the European survey of antimicrobial resistance with modifications. The survey was conducted from 8 AM to 8 PM daily within 2 weeks.Results: A total of 300 patients received antimicrobials and the prevalence rate of antimicrobial prescription was 79.15%. The major indications of antimicrobials were surgical prophylaxis followed by the treatment of community-acquired infection. The most commonly prescribed initial antimicrobial group was Aminopenicillin ± β-lactamase inhibitors. Although the purpose for antimicrobial administration was recorded in all cases, the stop/review history was recorded only in 19.6% and local guidelines were not available for 77.6% of antimicrobial prescriptions. The use of combined antimicrobials was common (46.6%), particularly in orthopedic and cardiothoracic surgery.Conclusion: The prevalence of antimicrobial prescription at MUH was high which requires serious actions including reviewing the antimicrobial indication, implementing local prescription guidelines, initiating an antimicrobial stewardship program (ASP), and optimizing infection control measures.Keywords: antimicrobial prescription pattern, Egypt, Mansoura, point prevalence survey, quality indicators

In the current paper, we aim to study the oscillatory behavior of a new class of third-order differential equations. In the present study, we are interested in a better understanding of the relationships between the solutions and their derivatives. The recursive nature of these relationships enables us to obtain new criteria that ensure the oscillation of all solutions of the studied equation. In comparison with previous studies, our results are more general and include models in a wider range of applications. Furthermore, our findings are also significant because no additional restrictive conditions are required. The presented examples illustrate the significance of the results.

The main objective of this work was to study some oscillatory and asymptotic properties of a new class of advanced neutral differential equations. Using new relations to link the solution and its corresponding function, we introduced new oscillatory criteria that aim to enhance, simplify, and complement some of current results. We provide some examples to demonstrate the significance of our results.

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution xs to its corresponding function zs and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations.

This paper presents an investigation into the qualitative behavior of solutions for a specific class of fourth-order half-linear neutral differential equations. The main objective of this study is to improve the relationship between the solution and its corresponding function. By developing improved relationships, a novel criterion is proposed to determine the oscillatory behavior of the studied equation. The exclusion of positive solutions is achieved through a comparative approach in which the examined equation is compared to second-order equations. Additionally, the significance of the obtained results is demonstrated by applying them to various illustrative examples.

Abstract In this work, we aim at studying the asymptotic and oscillatory behavior of even-order neutral delay noncanonical differential equations. To the best of our knowledge, most of the related previous works are concerned only with neutral equations in the canonical case. Our new oscillation criteria essentially improve, simplify, and complement related results in the literature, especially those from a paper by Li and Rogovchenko (Abstr. Appl. Anal. 2014:395368, 2014). Some examples are presented that illustrate the importance of the new criteria.

Abstract In this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

The objective of this work is to study the oscillatory behavior of neutral differential equations with several delays. By using both Riccati substitution technique and comparison with delay equations of first-order, we establish new oscillation criteria. Our new criteria are simplifying and complementing some related results that have been published in the literature. Moreover, some examples are given to show the applicability of our results.

We provide streamlined criteria for evaluating the oscillatory behavior of solutions to a class of higher-order functional differential equations in the non-canonical case. We use a comparison approach with first-order equations that have standard oscillation criteria. Normally, in the non-canonical situation, the oscillation test requires three independent conditions, but we provide criteria with two-conditions without checking the additional conditions. Lastly, we give examples to highlight the significance of the findings.

In this paper, we derive new properties for the decreasing positive solutions of half-linear delay differential equations of even order. The positive-decreasing solutions have a great influence on the study of qualitative properties, which include oscillation, convergence, etc.; therefore, we take care of finding sufficient conditions to exclude these solutions. In addition, we present new criteria for testing the oscillation of the studied equation.

In this work, in the noncanonical case, we find new properties for a class of positive solutions of fourth-order differential equations. These properties allow us to obtain iterative criteria that exclude positive decreasing solutions, and we then establish sufficient conditions to guarantee that all solutions to the examined equation oscillate. The importance of applying the results to a special case of the investigated equation is demonstrated.

Abstract The purpose of this work is to study the oscillation criteria for generalized Emden–Fowler neutral differential equation. We establish new oscillation criteria using both the technique of comparison with first order delay equations and the technique of Riccati transformation. Our new criteria are interesting as they improve, simplify, and complement some results that have been published recently in the literature. Moreover, we present an illustrating example.

Abstract In this paper, a class of 4th $4{th}$-order neutral delay differential equations with continuously distributed delay is studied. We establish a new oscillation criterion using the Riccati transformation. An example illustrating the results is also given.

Abstract In this work, new conditions are obtained for the oscillation of solutions of the even-order equation (r(ζ)z(n−1)(ζ))′+∫abq(ζ,s)f(x(g(ζ,s)))ds=0,ζ≥ζ0, $$ \bigl( r ( \zeta ) z^{ ( n-1 ) } ( \zeta ) \bigr) ^{\prime }+ \int _{a}^{b}q ( \zeta ,s ) f \bigl( x \bigl( g ( \zeta ,s ) \bigr) \bigr) \,\mathrm{d}s=0, \quad \zeta \geq \zeta _{0}, $$ where n≥2 $n\geq 2$ is an even integer and z(ζ)=xα(ζ)+p(ζ)x(σ(ζ)) $z ( \zeta ) =x ^{\alpha } ( \zeta ) +p ( \zeta ) x ( \sigma ( \zeta ) ) $. By using the theory of comparison with first-order delay equations and the technique of Riccati transformation, we get two various conditions to ensure oscillation of solutions of this equation. Moreover, the importance of the obtained conditions is illustrated via some examples.

In the present article, we iteratively deduce new monotonic properties of a class from the positive solutions of fourth-order delay differential equations. We discuss the non-canonical case in which there are possible decreasing positive solutions. Then, we find iterative criteria that exclude the existence of these positive decreasing solutions. Using these new criteria and based on the comparison and Riccati substitution methods, we create sufficient conditions to ensure that all solutions of the studied equation oscillate. In addition to having many applications in various scientific domains, the study of the oscillatory and non-oscillatory features of differential equation solutions is a theoretically rich field with many intriguing issues. Finally, we show the importance of the results by applying them to special cases of the studied equation.

Pristine films of polyvinyl alcohol (PVA)/polyvinyl pyrrolidone (PVP) polymer blend filled with gradient contents of (MWCNTs) multi-walled carbon nanotubes have been prepared using ordinary casting technique. Fourier transform infrared (FT-IR) revealed the existence of main characteristic peaks corresponding to vibrational groups that characterized the synthesized samples. The interaction between nano-composite components was indicated by variation of main vibrational bands in the spectral range 1500–1750 cm−1. X-ray diffraction (XRD) confirms the structural modification in PVA/PVP matrix due to MWCNTs filling. Transmission electron microscopy (TEM (shows the presence of MWCNTs with a diameter between 80 and 30 nm and length of about several micrometers. Scanning electron microscopy (SEM) used to approve the homogenous nature of prepared samples. The absorption coefficient spectra show the appearance of two absorption peaks at 290 and 620 nm attributed to n → π* and π → π* electronic transitions. The optical energy gap (Eg) have been obtained from the indirect allowed transition. It was found that, Eg decrease with increasing MWCNTs content. Analysis of refractive index n showed a normal dispersion in the wavelength range 866–2500 nm, as well as an anomalous dispersion in the wavelength range 190–866 nm. The oscillator parameters (oscillator energy and dispersion energy) were calculated. The decrease in optical energy gap and the increase in refractive index due to filling with MWCNTs suppose the possibility of their use in optical devices. Keywords: MWCNTs, PVA, PVP, Refractive index, FTIR, UV/vis

Casting technique was used for preparation of polyethylene oxide (PEO)/polyvinyl pyrrolidone (PVP) (70/30 wt.%) films filled with different concentrations of gold nanoparticles (Au NPs). X-ray diffraction (XRD) pattern proved the semi-crystalline nature of the pristine and filled polymer blend. Fourier transform infrared (FT-IR) and Ultraviolet/Visible (UV/Vis.) analyses were used to retrace the structural and optical changes with increasing Au content. UV/Vis. analysis spectroscopy was utilized to calculate the optical properties such as optical energy gap Eg, refractive index n and Urbach energy Eu for blend/Au nanocomposite films. Scanning electron micrograph (SEM) suggested the dependence of morphological structure on filling level and the surface morphology changed from rough to smooth. Transmission electron microscope (TEM) micrographs showed that the size of Au NPs was increased with continuous filling in PEO/PVP. Thermogravimetric analysis (TGA) was performed to investigate the thermal stability for nanocomposite films. Keywords: PEO/PVP, Au NPs, FT-IR, Optical properties, TGA

In this work, we will derive new asymptotic properties of the positive solutions of the fourth-order neutral differential equation with the non-canonical factor. We follow an improved approach that enables us to create oscillation criteria of an iterative nature that can be applied more than once to test oscillation. In light of this, we will use these properties to obtain new criteria for the oscillation of the solutions of the studied equation. An example is given to show the applicability of the main results.

The present study concerns the oscillation of a class of third-order nonlinear delay differential equations with middle term. We offer a new description of oscillation of the third-order equations in terms of oscillation of a related well studied second-order linear differential equation without damping. By using the integral averaging technique, we establish new oscillation results for this equation. Some examples are provided to illustrate the main results.

In this paper, we consider a class of quasilinear third-order differential equations with a delay argument. We establish some conditions of such certain third-order quasi-linear neutral differential equation as oscillatory or almost oscillatory. Those criteria improve, complement and simplify a number of existing results in the literature. Some examples are given to illustrate the importance of our results.

Abstract The aim of this work is to study asymptotic properties of a class of fourth-order delay differential equations. Our results in this paper not only generalize some previous results, but also improve the earlier ones. Examples are considered to elucidate the main results.

The aim of this work is to present new oscillation results for a class of second-order delay differential equations with damping term. The new criterion of oscillation depends on improving the asymptotic properties of the positive solutions of the studied equation by using an iterative technique. Our results extend some of the results recently published in the literature.

Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimates for positive solutions of the studied equation, using an iterative technique. Moreover, the iterative technique allows us to test the oscillation, even when the related results fail to apply. By establishing new comparison theorems that compare the nth-order equations with one or a couple of first-order delay differential equations, we obtain new conditions for oscillation of all solutions of the studied equation. To show the importance of our results, we provide two examples.

In biology, Difference equations is often used to understand and describe life phenomenon through mathematical models. So, In this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case.

Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form \[r(t)\psi(x(t))|z'(t)|^{\alpha -1} z'(t)+ \int_a^b q(t,\xi)f(x(g(t,\phi)))d\sigma (\xi) =0,\quad t\gt t_0,\] where \(\alpha \gt 0\) and \(z(t)= x(t)+p(t)x(t-\tau)\). Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results.

In this article we study the oscillation of solutions to the third order nonlinear functional dynamic equation $$ L_{3}(x(t))+sum_{i=0}^{n}p_i(t)Psi_k{alpha_ki}(x(h_i(t)))=0, $$ on an arbitrary time scale $mathbb{T}$. Here $$ L_0(x(t))=x(t),quad L_k(x(t))=Big(frac{[ L_{k-1}x(t)]^{Delta }}{a_k(t)}Big)^{gamma_kk}, quad k=1,2,3 $$ with $a_1, a_2$ positive rd-continuous functions on $mathbb{T}$ and $a_{3}equiv 1$; the functions $p_i$ are nonnegative rd-continuous on $mathbb{T}$ and not all $p_i(t)$ vanish in a neighborhood of infinity; $Psi_k{c}(u)=|u|^{c-1}u$, $c>0$. Our main results extend known results and are illustrated by examples.

Oscillation criteria are obtained for all solutions of first-order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature. Some examples are considered to illustrate our main results.

This paper concerns the oscillation of solutions to the differential equation $$ (r(t) x'(t))'+ p(t) x'(t) + q(t) g( x(t) ) =0, $$ where $xg(x)$ greater than 0 for all $x eq 0$, $r(t)$ greater than 0 for $tgeq t_{0}$ greater than 0. No sign conditions are imposed on $p(t)$ and $q(t)$. Our results solve the open problem posed by Rogovchenko [27], complement the results in Sun [29], and improve a number of existing oscillation criteria. Our main results are illustrated with examples.

In this work, we study the oscillatory features of a class of neutral differential equations with multiple delays. We present novel oscillation conditions for this equation by using a comparison method. We create conditions that exclude the positive solution of the examined equation. Using the feature of symmetry between non-oscillatory solutions (positive and negative), these conditions also exclude negative solutions without adding additional restrictions. In our study, we take into account the even and odd cases of the order of the equation. Furthermore, we study the asymptotic properties in three different cases of functional coefficients. Our results are a fundamental extension and generalization of previous relevant findings, and this fact has been demonstrated through comparisons. [ABSTRACT FROM AUTHOR]