Delay Differential Systems Research Articles

The Newton–Cotes quadratures for solving a delay differential system

The Newton–Cotes quadratures for solving a delay differential system

Delayed Monetary Policy Effects in a Multi-Regime Cointegrated VAR(MRCIVAR)

The effectiveness of monetary policies under delayed policy impacts are explored. Initially, in the context of a differential delay system, the macro-finance link is investigated. The nonlinear macro system with delays gives rise to a time-delayed optimal control problem. The optimality conditions are then analyzed, and the control problem is numerically solved by discretization and optimization methods. These solutions suggest that with too much delay, destabilizing financial conditions may emerge, rendering the policy ineffective. Then the possibility of asymmetric adjustments to a long-run steady-state, in a non-stationary environment is explored using a multi-regime cointegrated VAR (MRCIVAR) model for both an interest rate cut, and a non-interest rate cut regime. Though the rate cuts may not perform well with too long of a delay, given diverse shocks, monetary policy still performs better in a rate cut regime. Given the perils of deteriorating financial conditions, the better stabilization properties in a rate cut regime are empirically validated through data for European countries and the US.

Directional bionic underwater communication method using a parametric acoustic array and recursive filtering

This paper presents a bionic method for directional covert underwater communication using a parametric acoustic array. This technique can improve the concealment of communication and reduce the probability of its interception, combining the advantages of an underwater parametric acoustic array (low frequency, high directivity, and small size) and marine biological acoustics. Achieving appropriate pre-modulation of the excitation signal is the core of communication with a parametric array due to the nonlinear physical process of self-demodulation. To solve this problem, this the state equation and observation equation are constructed based on the Berktay equation of the parametric matrix, and a recursive Kalman filter modulation method is proposed to approach distortion-free transmission. The algorithm has low computational complexity and is conducive to real-time modulation. More importantly, it can suppress noise in the input signal and reduce its impact on the modulation effect. Using this method, a dolphin whistle signal is transmitted by the parametric array as the symbol for a pattern time delay difference system, which achieves the intended purpose of enhancing the concealment of the communication. The results from simulations and pool experiments show that the system is effective and feasible.

Finite time stability for nonsingular impulsive first order delay differential systems

This primer article focuses on the representation of solutions and finite-time stability of impulsive first-order delay differential systems. We define delayed matrix function with impulses and use variation of parameters to obtain a representation of solutions of linear systems with impulse effects. The famous classical Grownwall inequalities and properties of delayed matrix exponential with impulses are used to develop sufficient conditions for finite-time stability. In the end, we provide some examples to support the results.

The Analysis of Fractional‐Order System Delay Differential Equations Using a Numerical Method

To solve fractional delay differential equation systems, the Laguerre Wavelets Method (LWM) is presented and coupled with the steps method in this article. Caputo fractional derivative is used in the proposed technique. The results show that the current procedure is accurate and reliable. Different nonlinear systems have been solved, and the results have been compared to the exact solution and different methods. Furthermore, it is clear from the figures that the LWM error converges quickly when compared to other approaches. When compared with the exact solution to other approaches, it is clear that LWM is more accurate and gets closer to the exact solution faster. Moreover, on the basis of the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional‐order delay differential equations.

Robust uniform persistence for structured models of delay differential equations

<p style='text-indent:20px;'>We consider a general class of delay differential equations systems, typically used to model the dynamics of structured biological populations, and establish necessary conditions for the part of the attractor contained in the boundary of the state space to repel the complementary dynamics contained in the interior of the state space. The conditions are formulated in terms of Lyapunov exponents and invariant probability measures and we use them to prove a robust uniform persistence result.</p>

Swarming Computational Efficiency to Solve a Novel Third-Order Delay Differential Emden-Fowler System

The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks (ANNs) with the use of global search particle swarm optimization (PSO) along with the competent local search interior-point programming (IPP) called as ANN-PSOIPP. The proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model (TON-DD-EFM). The TON-DD-EFM is based on two types along with the particulars of shape factor, delayed terms, and singular points. A merit function is performed using the optimization of PSOIPP to find the solutions to the TON-DD-EFM. The effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the TON-DD-EFM. The scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−07. Furthermore, the statistical-based assessments for 100 trials are provided to compute the accuracy, stability, and constancy of the ANN-PSOIPP for solving the TON-DD-EFM.

Positive periodic solutions of delay differential system at resonance

This paper is devoted to the existence of positive periodic solutions for system of a class of nonlinear delay differential equations with periodic conditions. Our analysis is based on Mawhin coincidence degree theorem. An example is also presented to illustrate the effectiveness of the main result.

Results on controllability for Sobolev type fractional differential equations of order $ 1 < r < 2 $ with finite delay

<abstract><p>In this article, exact controllability results for Sobolev fractional delay differential system of $ 1 < r < 2 $ are investigated. Fractional analysis, cosine and sine function operators, and Schauder's fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.</p></abstract>

Existence of local and global solutions to fractional order fuzzy delay differential equation with non-instantaneous impulses

<abstract><p>The main concern of this manuscript is to examine some sufficient conditions under which the fractional order fuzzy delay differential system with the non-instantaneous impulsive condition has a unique solution. We also study the existence of a global solution for the considered system. Fuzzy set theory, Banach fixed point theorem and Non-linear functional analysis are the major tools to demonstrate our results. In last, an example is given to illustrate these analytical results.</p></abstract>

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays.

The presented study deals with the exploitation of the artificial intelligence knacks-based stochastic paradigm for the numerical treatment of the nonlinear delay differential system for dynamics of plant virus propagation with the impact of seasonality and delays (PVP-SD) model by implementing neural networks backpropagation with Bayesian regularization scheme (NNs-BBRS). The PVP-SD model is represented with five classes-based ODEs systems for the interaction between insects and plants. The nonlinear PVP-SD model governs with five populations: S(t) susceptible plants, I(t) infected plants, X(t) susceptible insect vectors, Y(t) infected insect vectors and P(t) predators. Adams numerical procedure is adopted to generate the reference solutions of the nonlinear PVP-SD model based on the variety of cases by varying the plants bite rate due to vectors, vector bite rate due to plants, plant’s recovery rate, predator contact rate with healthy insects, predator contact rate with infected insects and death rate caused by insecticides. The approximate solutions of the nonlinear PVP-SD model are determined by executing the designed NNs-BBRS through different target and inputs arbitrary selected samples for the training and testing data. Validation of the consistent precision and convergence of the designed NNs-BBRS is efficaciously substantiated through exhaustive simulations and analyses on mean square error-based merit function, index of regression and error histogram illustrations.

Non-instantaneous impulsive fractional-order delay differential systems with Mittag-Leffler kernel

<abstract><p>The existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations and the solution semigroup is not compact in Banach spaces. We suppose that the nonlinear term fulfills a non-compactness measure criterion and a local growth constraint. We further assume that non-instantaneous impulsive functions satisfy specific Lipschitz criteria. Finally, an example is given to justify the theoretical results.</p></abstract>

Supervised neural learning for the predator-prey delay differential system of Holling form-III

<abstract> <p>The purpose of this work is to present the stochastic computing study based on the artificial neural networks (ANNs) along with the scaled conjugate gradient (SCG), ANNs-SCG for solving the predator-prey delay differential system of Holling form-III. The mathematical form of the predator-prey delay differential system of Holling form-III is categorized into prey class, predator category and the recent past effects. Three variations of the predator-prey delay differential system of Holling form-III have been numerical stimulated by using the stochastic ANNs-SCG procedure. The selection of the data to solve the predator-prey delay differential system of Holling form-III is provided as 13%, 12% and 75% for testing, training, and substantiation together with 15 neurons. The correctness and exactness of the stochastic ANNs-SCG method is provided by using the comparison of the obtained and data-based reference solutions. The constancy, authentication, soundness, competence, and precision of the stochastic ANNs-SCG technique is performed through the analysis of the correlation measures, state transitions (STs), regression analysis, correlation, error histograms (EHs) and MSE.</p> </abstract>

Robustness and Delay Margin Analysis of a Gene Regulatory Network Model

In the past, a special type of nonlinear delay differential system structure was proposed for gene regulatory networks. For this cyclic dynamical system, stability analysis was done using various tools from systems theory. This paper investigates robust stability of an extended gene regulatory network model with time delayed negative feedback. Specifically, the delay margin analysis is done for this system under multiplicative uncertainty. The effect of uncertainty on the delay margin is determined. It is also shown that for particular higher order extensions of the model it is possible to improve the delay margin.

A two-dimensional discrete delay-differential system model of viremia.

A deterministic model is proposed to describe the interaction between an immune system and an invading virus whose target cells circulate in the blood. The model is a system of two ordinary first order quadratic delay-differential equations with stipulated initial conditions, whose coefficients are eventually constant, so that the system becomes autonomous. The long-term behavior of the solution is investigated with some success. In particular, we find two simple functions of the parameters of the model, whose signs often, but not always, determine whether the virus persists above a nonzero threshold in the circulation or heads toward extinction.

Simultaneous Stabilization of a Family of Delay Differential Systems by a Dynamic State Feedback

Simultaneous Stabilization of a Family of Delay Differential Systems by a Dynamic State Feedback

A general non-local delay model on oncolytic virus therapy

The oncolytic virus is regarded as a novel, powerful, and biologically safe method of cancer treatment. A general delay differential system was driven by the age-dependent model better to understand the interaction between tumor cells and viruses. General continuous functions F(x,y) and G(x) depict the tumor proliferation rate and virus infection rate. The critical threshold value R0 was calculated that plays a determinant role in whether virus therapy occurs. The non-local delay term ∫t−τtβG(x(θ))v(θ)e−α(t−θ)dθ makes our model hard to analyze when using the traditional eigenvalue method. The method combining implicit function theorem and comparison theorem is used to overcome this problem. Furthermore, we support the fact that virotherapy can lead to tumor remission by using the fluctuation method. Lastly, Bayesian information criterion was adopted to select a better model when fitting the experimental data.

Age-structure model for oncolytic virotherapy

A non-local delay differential system was developed by age-infected consideration to understand the interaction between tumor cells and oncolytic virus. The critical threshold value [Formula: see text] was obtained that dominates the dynamical behaviors of our model. By strongly [Formula: see text]-persistent and Comparison theorem, the global stability and uniformly strongly persistent were investigated. Our global sensitivity analyses indicate that [Formula: see text] is most sensitive to virus clearance rate [Formula: see text] while is least sensitive to viral life cycle [Formula: see text]. Finally, our model was used to fit with experimental data which indicates that viral life cycle [Formula: see text] plays a key role in data fitting. And the trained model shows perfect prediction in the testing data set with the coefficient of determination [Formula: see text].

Stability of delay differential systems under impulsive control suffered by logic choice

ABSTRACT This paper focuses on the stability of delay differential systems under impulsive control suffered by logic choice. Firstly, an impulsive control suffered by logic choice is constructed for a delay differential system to make it more suitable for some practical problems. Secondly, by using a semi-tensor product, an effective method for qualitative analysis, such as stability analysis, of a differential delay system under impulsive control suffered by logic choice is proposed. That is, the properties of a differential delay system under impulsive control suffered by logic choice can be obtained by the properties of a corresponding non-impulsive differential delay system. Thirdly, some stability criteria are obtained. Finally, three illustrative examples are also discussed.

(2010-6217) Solvability of fuzzy fractional stochastic Pantograph differential system

In this paper, a new type of equation namely fuzzy fractional stochastic Pantograph delay differential system (FSPDDS) is proposed. In our previous work, a first extension of fuzzy stochastic differential system into fuzzy fractional stochasticdifferential system by using Granular differentiability has been established. Here we study the existence and uniqueness results for the fuzzy FSPDDS which are obtained by using generalized Granular differentiability and contraction principlewith weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.