Nonlinear Analysis: Modelling and Control
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Synchronization analysis for stochastic multi-layer networks: Event-based impulsive control with predefined impulsive intervals
Full text linkThis article explores the novel approach to addressing the intra/inter-layer synchronization challenges in stochastic multi-layer networks (SMLNs). First, considering the influence of time delay in control, an event-triggered delayed impulsive control (ETDIC) strategy is developed, where the impulsive instant is determined by the predesigned event-triggered mechanism. Moreover, by introducing piecewise auxiliary functions, it effectively excludes Zeno behavior within the ETDIC framework. The study then derives sufficient conditions for ensuring intra- and inter-layer; synchronization, leveraging the Lyapunov method and rigorous mathematical analysis. Finally, theoretical results are validated through numerical simulations
Fixed point theory in RWC–Banach algebras
Full text linkIn this paper, we prove some fixed point results for the sum and the product of nonlinear continuous operators acting on an RWC–Banach algebra. Our result is formulated in terms of topological conditions on the operators. An illustrative example on an RWC–Banach algebra, which is not a WC–Banach algebra, is provided
Analysis and exact solutions for reaction–diffusion predator–prey system with prey-taxis by phi6 method
No full textThis article analyses the biomathematical model that describes the reaction–diffusion predator–prey system with prey-taxis. The analysis includes addressing the question of whether the solution exists and is unique. The next goal is to obtain the exact solutions. The ɸ6 method has been utilized for this purpose. The simulations of the obtained solutions are also incorporated, providing a broader understanding of the solutions
Spatiotemporal dynamics of a modified Leslie–Gower predator–prey model: Effects of diffusion and taxis-driven movements on pattern formation
Full text linkIn this manuscript, we investigate a Leslie–Gower predator–prey model with Crowley–Martin-type functional response. We also explore the dynamics of reaction–diffusion as well as reaction–diffusion–advection model. Specifically, our study focuses on an ecological model involving a generalist predator that induces fear, has carry-over effects, and experiences competitive interference. For the temporal model, a detailed mathematical analysis is carried out, investigating the positivity and boundedness of the solutions. We observe both monostability and bistability phenomena, and explore various local and global bifurcations by varying the fear and carry-over parameters. Interestingly, the fear and its carry-over effects have opposing roles in influencing stability within the temporal model. We incorporated prey-taxis into a general reaction–diffusion framework to represent the directed movement of predators towards regions with higher prey densities or when tracking signals such as scent to locate their prey. We perform the complete analysis of diffusion-driven and taxis-driven instability for reaction–diffusion and reaction–diffusion–advection models, respectively. Our findings emphasize the significant influence of predator diffusion and prey-taxis on pattern formation, revealing that increased random predator movement, combined with a moderate level of prey-taxis, can stabilize the model
Efficient computation of blood velocity in the left atrial appendage: A practical perspective
Full text linkThe goal of the paper is to present the FSI (fluid-structure interaction) CFD (computational fluid dynamics) simulations of the blood flow in the LA (left atrium) for patient-specific geometry of the left atrium appendage (LAA). These simulations are important for the decision making in cardiology and cardiac surgery of the patients with atrial fibrillation. Nowadays according current atrial fibrillation treatment guidelines, initiation of oral anticoagulant therapy is recommended for patients with a CHA2DS2–VASc score greater or equal to 2 for males, and greater or equal to 3 for females, for lowering stroke risk. This therapy although has undesirable effects and provokes bleeding in a part of cases. That is why it is important to detect the stagnation zones of the blood flow in LAA. The presence of such zones justifies the necessity of the anticoagulant therapy.
The FSI CFD simulations in the heart is a challenging problem: the existing softwares are not too robust for real life Reynolds numbers and often do not converge to the solution of the Navier–Stokes equations for the blood coupled with the elasticity equations of the wall. That is why we first provide the CFD computations with the rigid wall when the codes are more stable. Using this solution as a source of parameters for the implicit numerical scheme solver, we then provide the FSI computations, which become much more robust
Convergence analysis of positive solution for Caputo–Hadamard fractional differential equation
Full text linkBy deriving the expression of Green function and some of its special properties and establishing appropriate substitution and appropriate cone, the existence of unique iterative positive, error estimation, and convergence rate of approximate solution are obtained for singular p-Laplacian Caputo–Hadamard fractional differential equation with infinite-point boundary conditions. Nonlinearities involve derivative terms that make our analysis difficult in the course of this research, and we deal with the difficulty of derivative terms by making appropriate substitutions. An example is given to demonstrate the validity of our main results
On well-posedness and decay of Active model B
Full text linkWe study the well-posedness and decay estimates of Cauchy problem for Active model B in R3. First, based on the higher-order norm estimates of solutions and the mollifier technique, we obtain the local existence of unique strong solution. Then, by using pure energy method, one proves the global well-posedness and time decay estimates, provided that the H3/2-norm of initial data is sufficiently small
Bifurcation analysis of a Leslie–Gower predator–prey system with fear effect and constant-type harvesting
Full text linkThis paper investigates the effect of fear effect and constant-type harvesting on the dynamic of a Leslie–Gower predator–prey model. Initially, an analysis is carried out to identify all potential equilibria and evaluate their stability. Furthermore, the dynamic behavior at these points is examined, revealing various bifurcations such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation. In particular, the model undergoes a degenerate Hopf bifurcation, which leads to the existence of two limit cycles. Additionally, we demonstrate that the Bogdanov–Takens bifurcation of codimension 2 occurs in this model. Ultimately, these findings are validated through numerical simulations, demonstrating that continuous harvesting or the significant fear effect is not conducive to either predator or prey surviving
The finite-time ruin probabilities of a dependent bidimensional risk model with subexponential claims and Brownian perturbations
Full text linkThe paper considers a dependent bidimensional risk model with stochastic return and Brownian perturbations in which the price processes of the investment portfolio of the two lines of business are two geometric Lévy processes, and the claim-number processes of the two lines of business follows two different stochastic processes, which can be dependent. When the two components of each pair of claims from the two lines of business are strongly asymptotically independent and have subexponential distributions, the asymptotics of the finite-time ruin probability are obtained. Numerical studies are carried out to check the accuracy of the asymptotics of the finite-time ruin probability for the claims having regularly varying tail distributions
Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation
Full text linkThis paper introduces novel fixed-point theorems for generalized Proinov contraction mappings utilizing the measure of noncompactness. These results significantly extend existing contraction principles and provide novel methods for analyzing nonlinear problems. We demonstrate the practical power of our theorems by establishing the existence of solutions to a broad class of nonlinear fractional differential equations with integral boundary conditions. An illustrative example underscores the effectiveness of our approach, promising impactful applications in fractional calculus and nonlinear analysis. Overall, these results enrich the theoretical framework and offer valuable insights for researchers working on complex dynamical systems and applied mathematical models