Search results for "Applied Mathematics"
showing 10 items of 4379 documents
A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations
2019
We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
The arithmetic decomposition of central Cantor sets
2018
Abstract Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor sets of Lebesgue measure zero. Under some mild condition this result can be strengthened by stating that the summands can be chosen to be C s regular if the initial set is of this class.
Dynamical Models of Interrelation in a Class of Artificial Networks
2020
The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.
Solutions of nonlinear PDEs in the sense of averages
2012
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .
Painlevé analysis and exact solutions for the coupled Burgers system
2006
We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.
On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations
2020
Abstract By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument τ , our criteria improve a number of related results reported in the literature.
Relaxation for a Class of Control Systems with Unilateral Constraints
2019
We consider a nonlinear control system involving a maximal monotone map and with a priori feedback. We assume that the control constraint multifunction $U(t,x)$ is nonconvex valued and only lsc in the $x \in \mathbb{R}^{N}$ variable. Using the Q-regularization (in the sense of Cesari) of $U(t,\cdot )$, we introduce a relaxed system. We show that this relaxation process is admissible.
FROM DISCRETE KINETIC AND STOCHASTIC GAME THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES
2004
This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretization of the microscopic state generates a class of dynamical systems defining the evolution of the densities of the discretized state. In general, this yields a system of partial differential equations replacing the continuous integro-differential equation. As an example, a specific application is discussed, which refers to modelling in the field of…
A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems
2010
We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.