Nonlinear Analysis: Modelling and Control
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Stabilization of chaotic quaternion-valued neutral-type neural networks via sampled-data control with two-sided looped functional approach
Full text linkThe quaternion-valued neutral-type neural networks (QVNTNNs) stability problem through designing sampled-data controller is investigated in this paper. A main stability criterion of the considered neural networks (NNs) is obtained in the form of linear matrix inequalities (LMIs) based on the two-sided looped functional method. The effectiveness of the criterion is shown by a numerical example. It needs to be emphasized that the considered QVNTNNs model in this paper is not broken down into real-valued or complex-valued models in stability analysis, and the acquired criterion holds for both real-valued and complex-valued NNs
Results on integral inequalities for a generalized fractional integral operator unifying two existing fractional integral operators
Full text linkThe main aim of this article is to design a novel framework to study a generalized fractional integral operator that unifies two existing fractional integral operators. To ensure the suitable selection of the operator and with the discussion of special cases, it is shown that our considered fractional integral generalizes the well-known Atangana–Baleanu fractional integral (AB-fractional integral) and the ABK-fractional integral. Conditions are stated for the generalized AB-fractional integral operator (GAB-fractional integral operator) to be bounded in the space Xcp (γ1,γ2). We also provide a fractional product-integration formula for this operator. Furthermore, we generalize the reverse Minkowski’s inequality and the reverse Hölder-type inequality by utilizing the GAB-fractional integral operator. Additionally, some other types of integral inequalities are established, and several special cases are noted. The concepts in this article may influence further research in fractional calculus
Impact of multiple time delays on bifurcation of a class of fractional nearest-neighbor coupled neural networks
Full text linkIn this paper, the impacts of multiple time delays on bifurcation of a class of fractional nearest-neighbor coupled neural networks are considered. Firstly, the sum of time delays is selected as a parameter, and the fractional nearest-neighbor coupled neural network model is linearized to obtain the corresponding characteristic equation. Then, utilizing stability and bifurcation theory of fractional-order delay differential equations, we investigate the effect of time delays on the system’s stability and bifurcations. The results show that when the time lag exceeds the critical value, the system will lose stability and generate Hopf bifurcation. Finally, the correctness of the conclusions in this paper is verified through numerical simulation
Construction of the beta distributions using the random permutation divisors
Full text linkA subset of cycles comprising a permutation σ in the symmetric group Sn, n ∈ N, is called a divisor of σ. Then the partial sums over divisors with sizes up to un, 0 ≤ u ≤ 1, of values of a nonnegative multiplicative function on a random permutation define a stochastic process with nondecreasing trajectories. When normalized the latter is just a random distribution function supported by the unit interval. We establish that its expectations under various weighted probability measures defined on the subsets of Sn are quasihypergeometric distribution functions. Their limits as n -> 1 cover the class of two-parameter beta distributions. It is shown that, under appropriate conditions, the convergence rate is of the negative power of n order
On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations
Full text linkIn the present paper, a nonlinear system of sine-Gordon equations that describes the DNA dynamics is considered. A novel unconditionally stable second-order accuracy difference scheme corresponding to the system of sine-Gordon equations is presented. In this work, for the first time in the literature, weak solution of this difference scheme is studied. The existence and uniqueness of the weak solution for the difference scheme are proved in the space of distributions, and the methods of variational calculus are applied. The finite-difference method and the fixed point theory are used in combination to perform numerical experiments that verify the theoretical statements
Convective transport of pulsatile multilayer hybrid nanofluid flow in a composite porous channel
Full text linkMultilayer fluid models play a crucial role in comprehending fluid–fluid and fluid–nanoparticle interactions within the petroleum industry, geophysics, and plasma physics due to their diverse industrial applications. The current research aims to investigate the impact of a heat source/sink on a non-Newtonian hybrid nanofluid that saturates a porous medium positioned between a transparent viscous fluid filling a vertical channel. The model governing nonlinear coupled differential equations are nondimensionalized using appropriate fundamental quantities. Subsequently, the regular perturbation method is employed to solve the transformed dimensionless governing equations. Upon comparing the data, it is evident that current results closely align with the previously published findings. The parameter Q2 causes an increase in both θs(ζ) and θt(ζ) across all three regions. Increasing Casson parameter leads to a decrease in θt(ζ)
Existence of sunny nonexpansive retractions and approximation of fixed points of a representation of nonexpansive mappings
Full text linkThis paper presents an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth uniformly convex Banach space with respect to a left-regular sequence of means defined on a subset of l∞(S). The main results are to establish an existence theorem of a sunny nonexpansive retraction and to create an algorithm for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces
Exponential synchronization of dynamical complex networks via random impulsive scheme
Full text linkThis paper investigates the synchronization of a complex network based on a class of random impulsive differential equation systems. Based on the random impulsive strategy of Poisson distribution, a random impulsive dynamical network model is constructed. Using the Lyapunov principle, random process theory, linear matrix inequality method, and some basic analysis methods, we realize the global mean-square index synchronization of the model. We then get sufficient criteria for the synchronization. By presenting a numerical example, we verified the validity of the theoretical results
Investigation of solitons in magneto-optic waveguides with Kudryashov’s law nonlinear refractive index for coupled system of generalized nonlinear Schrödinger’s equations using modified extended mapping method
Full text linkIn this work, we investigate the optical solitons and other waves through magneto-optic waveguides with Kudryashov’s law of nonlinear refractive index in the presence of chromatic dispersion and Hamiltonian-type perturbation factors using the modified extended mapping approach. Many classifications of solutions are established like bright solitons, dark solitons, singular solitons, singular periodic wave solutions, exponential wave solutions, rational wave, solutions, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic function solutions. Some of the extracted solutions are described graphically to provide their physical understanding of the acquired solutions
Existence of solutions to a nonlinear fractional diffusion equation with exponential growth
Full text linkIn this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space