Nonlinear Analysis: Modelling and Control
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Global dissipativity and quasi-Mittag-Leffler synchronization of fractional-order complex-valued neural networks with time delays and discontinuous activations
Full text linkThis paper explores fractional-order complex-valued neural networks (FOCVNNs) with time delays and discontinuous activation functions. A novel fractional-order inequality is utilized to study this system as a whole without dividing it into different components in the complex plane. Firstly, the existence of global Filippov solutions in the complex domain is proven by using the theories of vector norms and fractional calculus. Next, some sufficient conditions are derived to ensure the global dissipativity and quasi-Mittag-Leffler synchronization of FOCVNNs through the use of nonsmooth analysis and differential inclusion theory. The error bounds of quasi-Mittag-Leffler synchronization are also estimated without relying on the initial values. Finally, some numerical simulations are conducted to demonstrate the effectiveness of the presented findings
Numerical algorithms to solve one inverse problem for Navier–Stokes equations
Full text linkThis model describes the Poiseuille type solution in the nonstationary case of the Navier–Stokes problem. An equivalent form of PDE problem is defined as the first-kind Volterra integral equation. The main aim is to analyze a possible ill-posedness of the given problem. For some problems the first-kind Volterra integral equation can be modified to the integral equation of the second kind and the letter equation is well-posed. Different regularization techniques also can be used to control the influence of error pollution with not equal efficiency. Thus we made an extensive analysis and compared classical discretization schemes for PDE and integral Navier–Stokes models and regularization algorithms.
The regularization methods are applied to control the influence of the noise in data. The numerical experiment was aimed at obtaining new information about the stability of schemes for the inverse problems. Different approximations methods are used to solve PDE and integral versions of the equation. Results of computational experiments are presented, they confirm the theoretical error analysis and stability estimates
On a novel type of generalized simulation functions with fixed point results for wide Ws-contractions
Full text linkOne of the most significant hypotheses in fixed point theory is the nonexpansivity condition of contractive mappings. This property is crucial as operators that do not satisfy this criterion may lack fixed points. In this paper, we propose a novel condition that, within the appropriate framework, can obviate the necessity of imposing the nonexpansivity requirement in the initial hypotheses. By employing this new condition, we illustrate how innovative results can be derived in this area. Finally, we examine the existence and uniqueness of a solution for an elastic beam equation with nonlinear boundary conditions grounded in the introduced fixed point results
Bifurcation in a Leslie–Gower system with fear in predators and strong Allee effect in prey
Full text linkIn this paper, we consider a modified Leslie–Gower predator–prey model with Allee effect on prey and fear effect on predators. Results show complex dynamical behaviors in the model with these factors. Existence of equilibrium points and their stability of the model are first given. Then it is found that, with the Allee and fear effects, the model exhibits various and different bifurcations, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. Theoretical analysis is verified through some numerical simulations
Existence of nontrivial solutions for a class of 2n-order ODE
Full text linkWe consider a semilinear 2n-order problem with nonconstant coefficients. We deduce existence results by using variational methods in two directions. We primarily treat the existence when the nonlinearity has asymptotic linear behaviour at infinity and is either asymptotically sublinear or linear at zero. Secondly, we discuss the superlinear case at infinity and prove three existence results showing that our problem has at least one or two nonzero solutions
Exploring fixed points via admissibility criteria for fuzzy theta f-weak contractions
No full textIn this study, we introduce a new class of fuzzy contractions, called fuzzy α-η-θf -weak contractions, and establish fixed point results within the framework of complete fuzzy metric spaces. A fuzzy metric space generalizes the concept of a metric space by defining the “distance” between two points ω and υ using a function ϑ(ω, υ, ς) that quantifies the degree of nearness between these points for a parameter ς > 0. This parameter ς reflects various factors influencing the closeness of the points, making fuzzy metric spaces a powerful tool for modeling uncertainty and imprecision in mathematical contexts. Based on this framework, we prove several fixed point theorems addressing the existence and uniqueness of fixed points for such contractions. By carefully selecting specific forms of the functions θf, α, and η, our primary results can be adapted to yield a variety of significant corollaries. Furthermore, our findings leverage admissible and auxiliary functions to provide a broader framework that consolidates, extends, and refines existing results in fixed point theory
Control of the servo motor using feedback linearization and artificial gorilla troops optimizer
Full text linkThis paper establishes a nonlinear optimization strategy for position control of a direct current motor. When experimental evidence showed that the linear model does not sufficiently represent the system, the model is modified from linear to nonlinear, using friction-induced nonlinearity. In the course of the research, an analysis of the nonlinear feedback linearizing controller and the up to date gorilla troops optimization algorithm are carried out. The proposed algorithm is juxtapose with four others metaheuristic optimizations. Furthermore, performances with and without different types of disturbances are compared for individual desired output signals. The experimental results corroborate the nonlinear control’s robustness
On stability and convergence of difference schemes for one class of parabolic equations with nonlocal condition
Full text linkIn this paper, we construct and analyze the finite-difference method for a two-dimensional nonlinear parabolic equation with nonlocal boundary condition. The main objective of this paper is to investigate the stability and convergence of the difference scheme in the maximum norm. We provide some approaches for estimating the error of the solution. In our approach, the assumption of the validity of the maximum principle is not required. The assumption is changed to a weaker one: the difference problem’s matrix is the M-matrix. We present numerical experiments to illustrate and supplement theoretical results
Exploring new exact solutions in the conformable time-fractional discrete coupled NLSE using a novel approach
Full text linkThis investigation focuses on the conformable time-fractional discrete coupled nonlinear Schrödinger system (CTFCDNLSEs). This system incorporates a fractional order represented as a conformable derivative. Through the application of the fractional transformation method (FTM), a set of novel analytical discrete solutions is derived. These solutions are characterized by an array of mathematical functions, including trigonometric, hyperbolic, and rational functions. Among these solutions, discrete fractional bright solitons, dark solitons, combined solitons, and periodic solutions stand out. To demonstrate the influence of the fractional-order parameter on the dynamics of fractional discrete solitons, graphical representations are provided. These findings are significant for exploring complex nonlinear discrete physical phenomena
A mathematical model for degradation of forest area by industrialization causing migration of wildlife species
Full text linkThis study presents a nonlinear mathematical model incorporating four key variables: forest area, biomass density, industrialization level, and wildlife population. The model assumes that biomass is proportional to forest area and that wildlife density depends on biomass availability. Our analysis demonstrates that increasing industrialization leads to significant forest depletion, which in turn accelerates wildlife migration. The results highlight critical thresholds beyond which forest degradation becomes irreversible, emphasizing the urgent need for sustainable industrial policies and conservation strategies. Numerical simulations and sensitivity analysis validate the model outcomes and provide insights for ecological preservation