Search Results (1,719)

The purpose of this paper is to study a predator–prey model with Allee effect and double time delays. This research examines the dynamics of the model, with a focus on positivity, existence, stability and Hopf bifurcations. The stability of the periodic solution and the direction of the Hopf bifurcation are elucidated by applying the normal form theory and the center manifold theorem. To validate the correctness of the theoretical analysis, numerical simulations were conducted. The results suggest that a weak Allee effect delay can promote stability within the model, transitioning it from instability to stability. Nevertheless, the competition delay induces periodic oscillations and chaotic dynamics, ultimately resulting in the population’s collapse. Full article

During anatomical dissection of a female body donor at the Howard University College of Medicine, a rare renal anomaly was discovered. Detailed anatomical and histological analyses on this anomaly were compared to a normal kidney from another donor and previously published reports from a comprehensive literature review. Anatomical assessment confirmed the condition of pancake kidney, a rare form of completely fused, ectopic kidneys without an isthmus. Due to the lack of symptoms in patients with this condition and the limited number of published case reports, very little information is available regarding the anatomy, development, and histology of pancake kidneys, making it difficult to determine an accurate estimate of the number of individuals who are affected. In the case presented here, a single kidney was located in the pelvis, below the bifurcation of the abdominal aorta into the common iliac arteries. The histological analysis of the pancake kidney revealed focal segmental glomerulosclerosis, dilated renal tubules, and increased interstitial fluid, all common characteristics of renal disease and not present in the normal kidney of the other donor. Future studies are needed to compare the histology of pancake kidneys and typical kidneys in order to help determine potential pathologies. Full article

Aiming to explore the subtle connection between the number of nonlinear terms in Lorenz-like systems and hidden attractors, this paper introduces a new simple sub-quadratic four-thirds-degree Lorenz-like system, where $\dot{x}=a(y-x)$, $\dot{y}=cx-\sqrt[3]{x}z$, $\dot{z}=-bz+\sqrt[3]{x}y$, and uncovers the following property of these systems: decreasing the powers of the nonlinear terms in a quadratic Lorenz-like system where $\dot{x}=a(y-x)$, $\dot{y}=cx-xz$, $\dot{z}=-bz+xy$, may narrow, or even eliminate the range of the parameter c for hidden attractors, but enlarge it for self-excited attractors. By combining numerical simulation, stability and bifurcation theory, most of the important dynamics of the Lorenz system family are revealed, including self-excited Lorenz-like attractors, Hopf bifurcation and generic pitchfork bifurcation at the origin, singularly degenerate heteroclinic cycles, degenerate pitchfork bifurcation at non-isolated equilibria, invariant algebraic surface, heteroclinic orbits and so on. The obtained results may verify the generalization of the second part of the celebrated Hilbert’s sixteenth problem to some degree, showing that the number and mutual disposition of attractors and repellers may depend on the degree of chaotic multidimensional dynamical systems. Full article

This study proposes and theoretically substantiates a unique mathematical model for predicting the spread of infectious diseases using the example of COVID-19. The model is described by a special system of autonomous differential equations, which has scientific novelty for cases of complex dynamics of disease transmission. The adequacy of the model is confirmed by testing on the example of the spread of COVID-19 in one of the largest regions of Ukraine, both in terms of population and area. The practical novelty emerges through its versatile application in real-world contexts, guiding organizational decisions and public health responses. The model’s capacity to facilitate system functioning evaluation and identify significant parameters underlines its potential for proactive management and effective response in the evolving landscape of infectious diseases. Full article

The Zika virus has been shown to infect glioblastoma stem cells via the membrane receptor ${\alpha }_v{\beta }_5$, which is activated by the stem-specific transcription factor SOX2. Since the expression level of SOX2 is an important predictive marker for successful virotherapy, it is important to understand the fundamental mechanisms of the role of SOX2 in the dynamics of cancer stem cells and Zika viruses. In this paper, we develop a mathematical ODE model to investigate the effects of SOX2 expression levels on Zika virotherapy against glioblastoma stem cells. Our study aimed to identify the conditions under which SOX2 expression level, viral infection, and replication can reduce or eradicate the glioblastoma stem cells. Analytic work on the existence and stability conditions of equilibrium points with respect to the basic reproduction number are provided. Numerical results were in good agreement with analytic solutions. Our results show that critical threshold levels of both SOX2 and viral replication, which change the stability of equilibrium points through population dynamics such as transcritical and Hopf bifurcations, were observed. These critical thresholds provide the optimal conditions for SOX2 expression levels and viral bursting sizes to enhance therapeutic efficacy of Zika virotherapy against glioblastoma stem cells. This study provides critical insights into optimizing Zika virus-based treatment for glioblastoma by highlighting the essential role of SOX2 in viral infection and replication. Full article

We discuss 1D, 2D and 3D bifurcation diagrams of two nonlinear dynamical systems: an electric arc system having both chaotic and periodic steady-state responses and a cytosolic calcium system with both periodic/chaotic and constant steady-state outputs. The diagrams are mostly obtained by using the 0–1 test for chaos, but other types of diagrams are also mentioned; for example, typical 1D diagrams with local maxiumum values of oscillatory responses (periodic and chaotic), the entropy method and the largest Lyapunov exponent approach. Important features and properties of each of the three classes of diagrams with one, two and three varying parameters in the 1D, 2D and 3D cases, respectively, are presented and illustrated via certain diagrams of the K values, $-1\le K\le 1$, from the 0–1 test and the sample entropy values $SaEn>0$. The K values close to 0 indicate periodic and quasi-periodic responses, while those close to 1 are for chaotic ones. The sample entropy 3D diagrams for an electric arc system are also provided to illustrate the variety of possible bifurcation diagrams available. We also provide a comparative study of the diagrams obtained using different methods with the goal of obtaining diagrams that appear similar (or close to each other) for the same dynamical system. Three examples of such comparisons are provided, each in the 1D, 2D and 3D cases. Additionally, this paper serves as a brief review of the many possible types of diagrams one can employ to identify and classify time-series obtained either as numerical solutions of models of nonlinear dynamical systems or recorded in a laboratory environment when a mathematical model is unknown. In the concluding section, we present a brief overview of the advantages and disadvantages of using the 1D, 2D and 3D diagrams. Several illustrative examples are included. Full article

Mathematical models such as Fitzhugh–Nagoma and Hodgkin–Huxley models have been used to understand complex nervous systems. Still, due to their complexity, these models have made it challenging to analyze neural function. The discrete Rulkov model allows the analysis of neural function to facilitate the investigation of neuronal dynamics or others. This paper introduces a fractional memristor Rulkov neuron model and analyzes its dynamic effects, investigating how to improve neuron models by combining discrete memristors and fractional derivatives. These improvements include the more accurate generation of heritable properties compared to full-order models, the treatment of dynamic firing activity at multiple time scales for a single neuron, and the better performance of firing frequency responses in fractional designs compared to integer models. Initially, we combined a Rulkov neuron model with a memristor and evaluated all system parameters using bifurcation diagrams and the 0–1 chaos test. Subsequently, we applied a discrete fractional-order approach to the Rulkov memristor map. We investigated the impact of all parameters and the fractional order on the model and observed that the system exhibited various behaviors, including tonic firing, periodic firing, and chaotic firing. We also found that the more I tend towards the correct order, the more chaotic modes in the range of parameters. Following this, we coupled the proposed model with a similar one and assessed how the fractional order influences synchronization. Our results demonstrated that the fractional order significantly improves synchronization. The results of this research emphasize that the combination of memristor and discrete neurons provides an effective tool for modeling and estimating biophysical effects in neurons and artificial neural networks. Full article

Background: Endovascular aortic aneurysm repair (EVAR) represents a valid treatment modality for ruptured abdominal aortic aneurysms (rAAAs). This study aimed to present rAAA outcomes treated by EVAR using the Endurant endograft. Methods: A single-center retrospective analysis of consecutive patients treated with standard EVAR (sEVAR) or parallel graft (PG)-EVAR for infra- or juxta/para-renal rAAA using the Endurant endograft (1 January 2008–31 December 2023) was undertaken. The primary outcomes were technical success, mortality, and reintervention. Follow-up outcomes, including survival and freedom from reintervention, were assessed using Kaplan–Meier estimates. Results: Eighty-eight patients were included (87.5% sEVAR and 12.5% PG-EVAR). The mean aneurysm diameter was 73.3 ± 19.3 mm (71.4 ± 22.2 mm sEVAR and 81.7 ± 33.0 mm PG-EVAR). Among 77 patients receiving sEVAR, 26 (33.8%) received an aorto-uni-iliac device. All PG-EVAR patients were managed with bifurcated devices, one receiving a single PG, seven double PGS, and three triple PGs. Technical success was 98.8% (100.0% sEVAR and 90.9% PG-EVAR). The 30-day mortality was 47.2% (50.7% sEVAR and 27.3% PG-EVAR), with nine (10.2%) deaths recorded on the table. The mean time of follow-up was 13 ± 9 months. After excluding 30-day deaths, the estimated survival was 75.5% (standard error (SE) 6.9%) at 24 months. The estimated freedom from reintervention was 89.7% (SE 5.7%) at 24 months. Only one endoleak type Ia event was recorded during follow-up. Conclusions: Endurant showed high technical success rates and low rates of endoleak type Ia events and reinterventions, despite the emergent setting of repair. rAAA is still a highly fatal condition within 30 days, with an acceptable mid-term survival of 30-day survivors at 75.5%. Full article

Polygonal wear affects driving safety and drastically shortens a wheel’s life. This work establishes a wheel–rail coupled system’s rotor dynamics model and a wheel polygonal wear model, taking into account the wheelset’s flexibility, the effect of the wheelset rotation, and the initial wheel polygon. The energy approach is applied to study the stability of the self-excited vibration of a wheel–rail coupled system. The wheel polygonal wear generation and evolution mechanism is revealed, along with the impact of vehicle and rail characteristics on a wheel’s high-order polygon. The findings demonstrate that wheel polygonal wear must occur in order for the wheel–rail system to experience self-excited vibration, which is brought on by a feedback mechanism dominated by creepage velocity. Additionally, the Hopf bifurcation characteristic is displayed by the wheel–rail system’s self-excited vibration. Wheel polygonal wear is characterized by “fixed frequency and integer division”, and the wheelset flexibility largely determines the fixed frequency of high-order polygonal wear, which is mostly unaffected by the suspension characteristics of the vehicle. By decreasing the tire load, increasing the wheelset’s damping, and choosing a variable running speed, the progression of polygonal wear on wheels can be prevented. Future investigations on the suppression of wheel polygonal wear evolution can be guided by the results. Full article

LMNA-related dilated cardiomyopathy (DCM) is an autosomal-dominant genetic condition with cardiomyocyte and conduction system dysfunction often resulting in heart failure or sudden death. The condition is caused by mutation in the Lamin A/C (LMNA) gene encoding Type-A nuclear lamin proteins involved in nuclear integrity, epigenetic regulation of gene expression, and differentiation. The molecular mechanisms of the disease are not completely understood, and there are no definitive treatments to reverse progression or prevent mortality. We investigated possible mechanisms of LMNA-related DCM using induced pluripotent stem cells derived from a family with a heterozygous LMNA c.357-2A>G splice-site mutation. We differentiated one LMNA-mutant iPSC line derived from an affected female (Patient) and two non-mutant iPSC lines derived from her unaffected sister (Control) and conducted single-cell RNA sequencing for 12 samples (four from Patients and eight from Controls) across seven time points: Day 0, 2, 4, 9, 16, 19, and 30. Our bioinformatics workflow identified 125,554 cells in raw data and 110,521 (88%) high-quality cells in sequentially processed data. Unsupervised clustering, cell annotation, and trajectory inference found complex heterogeneity: ten main cell types; many possible subtypes; and lineage bifurcation for cardiac progenitors to cardiomyocytes (CMs) and epicardium-derived cells (EPDCs). Data integration and comparative analyses of Patient and Control cells found cell type and lineage-specific differentially expressed genes (DEGs) with enrichment, supporting pathway dysregulation. Top DEGs and enriched pathways included 10 ZNF genes and RNA polymerase II transcription in pluripotent cells (PP); BMP4 and TGF Beta/BMP signaling, sarcomere gene subsets and cardiogenesis, CDH2 and EMT in CMs; LMNA and epigenetic regulation, as well as DDIT4 and mTORC1 signaling in EPDCs. Top DEGs also included XIST and other X-linked genes, six imprinted genes (SNRPN, PWAR6, NDN, PEG10, MEG3, MEG8), and enriched gene sets related to metabolism, proliferation, and homeostasis. We confirmed Lamin A/C haploinsufficiency by allelic expression and Western blot. Our complex Patient-derived iPSC model for Lamin A/C haploinsufficiency in PP, CM, and EPDC provided support for dysregulation of genes and pathways, many previously associated with Lamin A/C defects, such as epigenetic gene expression, signaling, and differentiation. Our findings support disruption of epigenomic developmental programs, as proposed in other LMNA disease models. We recognized other factors influencing epigenetics and differentiation; thus, our approach needs improvement to further investigate this mechanism in an iPSC-derived model. Full article

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters. Full article

Coronary bifurcation lesions account for a significant proportion of all percutaneous coronary interventions (PCIs). Interventional treatment of coronary bifurcations is related to significant technical challenges, high complication rates, and worse angiographic and long-term clinical outcomes. This review covers the specific features and structure of coronary bifurcation and explores the main challenges in the interventional treatment of these lesions. This review evaluates various methodologies designed to address these lesions, considering factors such as plaque distribution and bifurcation geometry. It also emphasizes the limitations associated with current techniques. A novel combined optimization approach applied in the interventional treatment of coronary bifurcation may offer superior procedural and long-term outcomes. This combined technique could potentially address the drawbacks of each method, providing a more effective solution for optimizing stent placement in bifurcation lesions. Refining and evaluating these combined techniques is essential for improving clinical outcomes in patients with bifurcation lesions. Full article

In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables to both reduce the number of parameters as well as bring symmetry to the isoclines of the mapping. With this new model, we demonstrate the existence of a forward invariant and globally attracting set where all the dynamics occur. In this set, the model possesses two symmetric fixed points: the origin, which is always a saddle fixed point, and an interior fixed point that may be globally asymptotically stable. Moreover, we observe the presence of a supercritical Neimark–Sacker bifurcation, a phenomenon that is not present in the original non-evolutionary model. Full article

In this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles. For the first class of systems, there exist $2n+1$ limit cycles, which include an algebraic limit cycle and $2n$ small limit cycles. For the second class of systems, there exist $\frac{n^2+3n+2}{2}$ limit cycles, including an algebraic limit cycle and $\frac{n^2+3n}{2}$ small limit cycles. Full article

The Shisong lü 十誦律, translated in the early 5th century, remains the only complete version of this Buddhist Vinaya text preserved to date and represents the first Vinaya text translated into Chinese. This Vinaya text introduced standardized terminology that significantly influenced subsequent translations of Vinaya texts and profoundly impacted Chinese Buddhism during the Six Dynasties period. Due to its complex translation history, the text is bifurcated into two lineages: the Northern lineage, featuring an initial 58-scroll version (without a preface), and the Southern lineage, with an expanded 61-scroll version (including a preface). This study examines the two oldest extant manuscripts of the Lüxu 律序 (Preface to the Shisong lü) from the Southern lineage—one from the Dunhuang collection currently preserved in Japan and the other from the Nara Japan. Through intensive comparisons with woodblock editions, these manuscripts from Dunhuang, and ancient Japanese manuscript Buddhist canons, this study not only traces the textual evolution of the Southern lineage of the Shisong lü from the 6th to the 13th centuries but also offers new insights into both the historical development and the relationship between these two lineages of the text. Methodologically, this paper provides inspiration for textual criticism of the Vinaya in particular and Buddhist studies in general. Full article