# جستجوی مقالات مرتبط با کلیدواژه « delay » در نشریات گروه « ریاضی »

تکرار جستجوی کلیدواژه « delay » در نشریات گروه « علوم پایه »
• Naoufel Hatime, Said Melliani, Ali El Mfadel *, Mhamed Elomari
In this paper, we study the existence, uniqueness, and finite-time stability results for fractional delayed Newton cooling law equation involving Ψ-Caputo fractional derivatives of order α ∈ (0, 1). By using Banach fixed point theorem, Henry Gronwall type retarded integral inequalities, and some techniques of Ψ-Caputo fractional calculus, we establish the existence and uniqueness of solutions for our proposed model. Based on the heat transfer model, a new criterion for finite time stability and some estimated results of solutions with time delay are derived. In addition, we give some specific examples with graphs and numerical experiments to illustrate the obtained results. More importantly, the comparison of model predictions versus experimental data, classical model, and non-delayed model shows the effectiveness of our proposed model with a reasonable precision.
Keywords: Newton’s law of cooling equation, Ψ-Caputo fractional derivative, delay, modelling nature}
• Chunhua Feng

A five coupled Kaldor-Kalecki economic model with one delay appeared in the literature, in which the periodic solution of the model was verified by numerical analysis. The periodic solution is an important characteristic of the mutual interactions of economic systems. Also, different investment functions may have different delays. The present paper extends the five coupled Kaldor-Kalecki economic model with one delay to a multiple delay system and discusses the existence of periodic oscillation of this multiple delay model. By linearizing the investment functions at the positive equilibrium and analyzing the instability of the positive equilibrium together with the boundedness of the solutions, some sufficient conditions to guarantee the existence of periodic oscillatory solutions for this model are established. Computer simulations are given to illustrate the validity of the theoretical results. The present result is new.

Keywords: economic model, delay, instability, periodic oscillation}
• Sultan Erdur, Cemil Tunc *
This work deals with the existence of periodic solutions (EPSs) to a third order nonlinear delay differential equation (DDE) with multiple constant delays. For the considered DDE, a theorem is proved, which includes sufficient criteria related to the EPSs. The technique of the proof depends on Lyapunov-Krasovskiˇı functional (LKF) approach. The obtained result extends and improves some results that can be found in the literature. In a particular case of the considered DDE, an example is provided to show the applicability of the main result of this paper.
Keywords: existence, periodic solutions, Differential equation, third order, delay, LKF}
• Chunhua Feng, Cadavious Jones *
It is known that the original Kaldor-Kalecki model of business cycle was an example of a difference differential model. In the literature there are many results about this model and how it relates to an extended form representing an economic growth model and how the role of government and its simultaneous monetary, fiscal policies can affect the economic stability. The authors proposed and studied business models using ordinary differential equations, nonlinear investment and saving functions. They showed that periodic solutions exist under the assumption of nonlinearity. Since then, similar models were also analyzed by several researchers and the existence of limit cycles was established due to the nonlinearity. In this paper, a three coupled Kaldor-Kalecki model with multiple delays is investigated. By means of the generalized Chafee’s criterion, some sufficient conditions to guarantee the existence of oscillatory solution for the model are obtained. Computer simulations are provided to demonstrate the proposed results.
Keywords: three coupled Kaldor-Kalecki model, Delay, Instability, limit cycle}

In this paper, we consider a system of viscoelastic wave equations of Kirchhoff type with delay and logarithmic nonlinearity. We obtain the local existence of solution by using the Faed-Galerkin approximation and under suitable conditions, we prove the blow up of solutions in finite time.

Keywords: Wave Equation, Local existence, blow up, logarithmic nonlinearity, Delay}
• M. Manikandan*, K. Ratnavelu, P. Balasubramaniam, S. H. Ong

This paper deals with the synchronization problem of bidirectional associative memory (BAM) Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with discrete time-varying and unbounded distributed delays. Some sufficient conditions are obtained to guarantee the robust synchronizationof BAM CGFCNNs with discrete time-varying and unbounded distributed delays subjected to parametric uncertainty by using Lyapunov-Krasovskii (LK) functional and Linear matrix inequality (LMI) approach.Sufficient criteria ensure that the error dynamics of considered system is globally asymptotically stable. Finally, numerical examples with simulations are given to show the efficacy of the derived results.

Keywords: Linear matrix inequality, fuzzy cellular neural networks, delay, synchronization, Cohen-Grossberg neuralnetworks}
• V. Chowthri, A. Uma *, P. Kalpana

• Ahmadreza Ghaznavi, SMT Almodarresi *
This research investigates the delay sensitivity of discrete-time consensus among agents which communicate over a scale-free network with hubs. In this paper, a novel hierarchical consensus algorithm, based on the idea of virtual communication graph degree reduction, is proposed. As a result, a significant consensus speed gain is obtained which provides a potential time margin for applying cyber-physical techniques that cause systematic input delay. This approach provides robustness and resiliency in case of any communication topology disturbance during cyber- physical attacks or plug-and-play events. The feasibility of plug- and-play, which has the potential to increase the input delay, is presented based on the gained margin as a sample scenario. The algorithm application in the coordination of distributed photovoltaic resources of several nano-grids communicating over a scale-free network, is assessed via simulation as well.
Keywords: Discrete-time consensus, delay, DC nano-grid, hierarchical control, multi-agent system, network with hub, plug- and-play, robust, resilient consensus, scale-free network}
• Rishi Tuli *, Joydip Dhar, Harbax Bhatti
In this paper, an economic group delay model is established. Dynamical behavior and Basic influence number of the proposed system are studied. Asymptotic stability analysis is carried out for the steady-states. The critical value of the delay \$tau\$ is determined. It is observed that for the interior steady-state remains stable if the adoption delay for the low-income group is less than the threshold value, i.e., \$tau<tau_{0}^+\$. If \$tau\$ crosses its threshold, system perceives oscillating behavior, and Hopf bifurcation occurs. Moreover, sensitivity analysis is performed for the system parameter used in the interior steady-state. Finally, numerical simulations are conducted to support our analytical findings.
Keywords: Boundedness, positivity, delay, Hopf bifurcation, sensitivity analysis}
• Liu Cui *, Yanchai Liu, Yueying Wang, Dengping Duan
This paper is concerned with delay-dependent exponential stability analysis and stabilization for continuous-time T-S fuzzy Markovian jump systems with mode-dependent time-varying delay. By constructing a novel Lyapunov-Krasovskii functional and utilizing some advanced techniques, less conservative conditions are presented to guarantee the closed-loop system is mean-square exponentially stable. Then, the stabilization conditions are derived and the fuzzy controller can be obtained by solving a set solutions of LMIs. The upper bound of time-delay that the system can be stabilized is given by using an optimal algorithm. Two examples are presented to illustrate the effectiveness and potential of our methods.
Keywords: Delay, dependent exponential stability, stabilization, Fuzzy systems, Lyapunov, Krasovskii functional, Markovian jump systems, Mode, dependent time delay}
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