State-dependent Delay Research Articles

Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families

In this work, we study the existence solutions and the dependence continuous with the initial data for some nondensely nonautonomous partial functional differential equations with state-dependent delay in Banach spaces. We assume that the linear part is not necessarily densely defined, satisfies the well-known hyperbolic conditions and generate a noncompact evolution family. Our existence results are based on Sadovskii fixed point Theorem. An application is provided to a reaction-diffusion equation with state-dependent delay.

Nonlocal partial fractional evolution equations with state dependent delay

In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions.

Controllability Analysis of Impulsive Multi-Term Fractional-Order Stochastic Systems Involving State-Dependent Delay

This study deals with the controllability of multi-term fractional-order stochastic systems with impulsive effects and state-dependent delay that exhibit damping behavior. Based on fractional calculus theory, the Caputo fractional derivative is utilized to analyze the controllability of fractional-order systems. Mittag–Leffler functions and Laplace transform are used to derive the solution set of the problem. Sufficient conditions for the controllability of nonlinear systems are achieved using fixed-point techniques and stochastic theory. Finally, the results stated in the paper are validated using examples.

Approximate controllability of time‐varying measure differential problem of second order with state‐dependent delay and noninstantaneous impulses

It is comprehended that the systems without any limitation on their Zeno action are enthralled in a vast class of hybrid systems. This article is influenced by a new category of nonautonomous second‐order measure differential problems with state‐dependent delay (SDD) and noninstantaneous impulses (NIIs). Some new sufficient postulates are created that guarantee the solvability and approximate controllability. We employ the fixed point strategy and theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. The measure of noncompactness is applied to establish the existence of a solution. Moreover, the measured differential equations generalize the ordinary impulsive differential equations. Thus, our findings are more prevalent than that encountered in the literature. At last, an example is comprised that exhibits the significance of the developed theory.

Stability Switches, Hopf Bifurcation and Chaotic Dynamics in Simple Epidemic Model with State-Dependent Delay

Dynamic behavior investigations of infectious disease models are central to improve our understanding of emerging characteristics of model states interaction. Here, we consider a Susceptible-Infected (SI) model with a general state-dependent delay, which covers an immuno-epidemiological model of pathogen transmission, developed in our early study, using a threshold delay to examine the effects of multiple exposures to a pathogen. The analysis in the previous work showed the appearance of forward as well as backward bifurcations of endemic equilibria when the basic reproductive ratio [Formula: see text] is less than unity. The analysis, in the present work, of the endemically infected equilibrium behavior, through the study of a second order exponential polynomial characteristic equation, concludes the existence of a Hopf bifurcation on the upper branch of the backward bifurcation diagram and gives the criteria for stability switches. Furthermore, the inclusion of state-dependent delays is shown to entirely change the dynamics of the SI model and give rise to rich behaviors including periodic, torus and chaotic dynamics.

Solving Coupled Impulsive Fractional Differential Equations With Caputo-Hadamard Derivatives in Phase Spaces

In this manuscript, we incorporate Caputo-Hadamard derivatives in impulsive fractional differential equations to obtain a new class of impulsive fractional form. Further, the existence of solutions to the proposed problem has been inferred under a state-dependent delay and suitable hypotheses in phase spaces. Finally, the considered problem has been supported by an illustrative application.

Existence Results for Some Functional Integrodifferential Equations with State-Dependent Delay

Existence Results for Some Functional Integrodifferential Equations with State-Dependent Delay

New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses

This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces. Our objective is to establish adequate conditions that ensure the existence, uniqueness, and Ulam–Hyers–Rassias stability results for our problems. The studied problems encompass abstract impulsive fractional differential problems with finite delay, infinite delay, state-dependent finite delay, and state-dependent infinite delay. To provide clarity and depth, we augment our theoretical results with illustrative examples, illustrating the practical implications of our work.

Nonlinear dynamics of a drillstring system with PDC bit in curved wells based on the finite element method

In this paper, a nonlinear mathematics model for axial-torsional-lateral dynamics of drillstring system equipped with a PDC bit in curved wells is established and analyzed. In the proposed model, using the finite element method, the drillstring structure is spatially discretized by Euler-Bernoulli beam elements with twelve degrees of freedom. Based on rock surface morphology of bit-rock interaction, a more realistic cutting and friction model with state-dependent delay effects is introduced to represent the bit-rock interaction. Meanwhile, a new top boundary condition is proposed to simulate the desired weight on bit (WOB). The nonlinear dynamic model is discretized in time-domain employing the generalize-α method, and the modified Newton iteration method is employed to calculate displacement response at the while-time step. Finally, the parametric analysis is carried out for discussing the influences of weight on bit and rotating speed on the nonlinear vibration of the drillstring system, respectively.

Infinitely Many Positive Solutions to Nonlinear First-Order Iterative Systems of Singular BVPs on Time Scales

Iterative differential equations provide a new idea to study functional differential equations. The study of iterative equations can provide new methods for the study of differential equations with state-dependent delays. In this paper, we are concerned with proving the existence of infinitely many positive solutions to nonlinear first-order iterative systems of singular BVPs on time scales by using Krasnoselskii’s cone fixed point theorem in a Banach space. It is worth pointing out that in this paper, we can use the symmetry of the iterative process and Green’s function to transform the considered differential equation into an equivalent integral equation, which plays a key role in the proof of the theorem in this paper.

Computational method for feedback perimeter control of multiregion urban traffic networks with state-dependent delays

Perimeter control is the manipulation of traffic flow by adjusting traffic signals on the borders between regions. It can be used to address the problem of traffic congestion in urban areas. Although there are many papers devoted to perimeter control, the dependence of time delay on traffic state is rarely considered. Moreover, most of them depend on accumulation reference points of the network and the stability of given equilibrium points to derive a perimeter controller. In reality, such equilibrium points and the optimal reference points are unavailable in advance. With these in minds, this paper formulates an optimal feedback perimeter control problem (OFPCP) subject to state-dependent delays without given information about the optimal reference point and equilibrium point. Different from the control method based on linearization or partial linearization, a hybrid algorithm combining filled function method and gradient-based method is introduced to solve this challenging optimal feedback control problem. Some experiments are performed to demonstrate the effectiveness of our method.

Existence results on nonautonomous partial functional differential equations with state-dependent infinite delay

The aim of this work is to establish the existence of mild solutions for some nondensely nonau-tonomous partial functional differential equations with state-dependent infinite delay in Banachspace. We assume that, the linear part is not necessarily densely defined and generates an evolution family under the hyperbolique conditions. We use the classic Shauder Fixed Point Theorem, the Nonlinear Alternative Leray-Schauder Fixed Point Theorem and the theory of evolution family, we show the existence of mild solutions. Secondly, we obtain the existence of mild solution in a maximal interval using Banach’s Fixed Point Theorem which may blow up at the finite time, weshow that this solution depends continuously on the initial data under the global Lipschitz condition on the second argument of F and we get the existence of global mild solution. We proposesome model arising in dynamic population for the application of our results.

New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay

New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay

Approximate Controllability of Nonlinear Fractional Stochastic Systems Involving Impulsive Effects and State Dependent Delay

This paper studies the analysis of approximate controllability for the fractional order neutral stochastic impulsive integro-differential systems involving nonlocal condition and State Dependent Delay (SDD). Sufficient conditions are designed to illustrate the evaluation of approximate controllability. It is exhibited that the proposed protocol can explicitly drive the results by Krasnoselskii's fixed point technique and semigroup theory. As a final point, the derived scheme is validated through an example.

Some sufficient conditions of existence and trajectory controllability for impulsive and initial value fractional order functional differential equations

For a class of impulsive fractional differential equation with fractional order r∈(1,2) by means of solution operator Sr(t), we develop the mild solution and deal with the existence results of mild solution for the considered equation with state-dependent delay through three fixed point theorems, namely Banach, Nonlinear Leray–Schauder Alternative and Krasnoselskii’s fixed point theorem. Next, we define the mild solution via an operator function Wr,β(τ) for abstract version of the considered equation. Further, we study the trajectory controllability (which is a stronger notion than other controllability) of the equation. In the last, we present some examples to illustrate the established results through partial fractional differential equations.

Explicit abstract neutral differential equations with state-dependent delay: Existence, uniqueness and local well-posedness

We study the local and global existence and uniqueness of strict solution and the local well-posedness for a class of abstract “explicit” neutral integro-differential equations with state-dependent delay. In the last section some examples motivated by explicit neutral ordinary integro-differential equations arising in the theory of population dynamics are presented.

Optimal condition for asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation

We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation c > 0 {\mathfrak {c}}>0 under minimal (i.e., necessary) assumptions on the influence function. In particular, we assume that the influence function is globally positive, which is necessary for reaching global consensus, and such that the agents move with speeds strictly less than c {\mathfrak {c}} , which is necessary for well-posedness of solutions. From this point of view, our result is optimal. The proof is based on the fact that the state-dependent delay, induced by the finite speed of information propagation, is uniformly bounded.

Global Hopf Bifurcation of State-Dependent Delay Differential Equations

We apply the [Formula: see text]-equivariant degree method to a Hopf bifurcation problem for functional differential equations with a state-dependent delay. The formal linearization of the system at a stationary state is extracted and translated into a bifurcation invariant by using the homotopy invariance of [Formula: see text]-equivariant degree. As a result, the local Hopf bifurcation is detected and the global continuation of periodic solutions is described.

Approximate controllability of second-order impulsive neutral stochastic differential equations with state-dependent delay and Poisson jumps

We consider the approximate controllability for a class of second-order impulsive neutral stochastic differential equations with state-dependent delay and Poisson jumps in a real separable Hilbert space. Under the sufficient conditions, we obtain approximate controllability results by virtue of the theory of a strongly continuous cosine family of bounded linear operators combined with stochastic inequality technique and the Sadovskii fixed point theorem. Finally, we illustrate the main results by an example.

Approximate Controllability of Neutral Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulses

In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies on the utilization of resolvent operators in conjunction with Darbo’s fixed point theorem. To exemplify the practical implications of our findings, we provide an illustration.