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This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen-Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

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In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays. By utilizing the normal form theory and the center manifold theorem, we investigated the direction and stability of these periodic solutions. Our theoretical findings were validated through numerical simulations, which demonstrated that the fear delay could trigger a stability shift at the positive equilibrium. Additionally, we observed that an increase in fear intensity or the presence of substitute prey reinforces the stability of the positive equilibrium.

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This article investigates the asymptotic stability of a general class of fractional-order multiple delayed systems to evaluate the delay robustness. We establish a one-to-one spectral connection between the original fractional-order system and the transformed one under the power mapping. The applicability of the Cluster Treatment of Characteristic Roots paradigm to the transformed dynamics is proved by this connection. Then, we utilize the Dixon resultant-based frequency sweeping framework to create the complete stability map. The results demonstrate that the order adjustment control significantly enhances the control flexibility and brings unlimited possibilities for the improvement of the delay robustness. Finally, we inspect the stability preservation problem when using the integer-order approximations for practical implementation.

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OBJECTIVE: This study aimed at providing a national prevalence of single and multiple developmental delays (DDs) among 41,640 Egyptian children aged 1 to 12 years and exploring DDs' associated risk and protective factors. METHODS: A national household survey from eight governorates of Egypt representing the four major subdivisions of Egypt was conducted through systematic probability proportionate to size. All enrolled children were assessed according to Vineland Adaptive Behavior Scales, (VABS) as a reliable screening questionnaire for identifying categories of DDs that were verified by pediatrics' specialists. RESULTS: The overall prevalence of children with DDs was 6.7%. The prevalence of a single DD was 3.9% versus 2.8% multiple DDs. Communication deficit was the most prevalent type (5.3%). Lower prevalence was identified for fine motor delay (1.0%), gross motor delay, and socialization deficit (1.5% each). Whereas deficits in daily life skills (self-help and adaptive behavior delay) amounted to 2.3%. Living without mothers and/or fathers in homes was associated with increased odds of having DDs by one and a half times (OR = 1.72 and OR = 1.34 respectively). Multiple logistic regression analysis revealed the most predictors for DDs including children who suffer from convulsions after birth (OR = 3.10), low birth weight babies (OR = 1.94), male sex (OR = 1.75), mothers having health problems during pregnancy (OR = 1.70) and belonging to middle socioeconomic status (OR = 1.41). Children who suffered from cyanosis after birth was found to be at risk for any or multiple DDs. Difficult labor was significantly associated with increased odds for multiple DDs (OR = 1.55). Higher paternal and maternal education was associated with decreased odds to have any DDs by 40% (OR = 0.60 and OR = 0.58 respectively). CONCLUSIONS: The detected prevalence of DDs is within the estimated range of prevalence of DDs for the pediatric population. The majority of the detected risk factors are preventable. Developmental screening is recommended to be implemented in all primary care settings as a routine practice.

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This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays.

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This paper deals with the synchronization for discrete-time coupled neural networks (DTCNNs), in which stochastic perturbations and multiple delays are simultaneously involved. The multiple delays mean that both discrete time-varying delays and distributed delays are included. Time-triggered impulsive control (TTIC) is proposed to investigate the synchronization issue of the DTCNNs based on the recently proposed impulsive control scheme for continuous neural networks with single time delays. Furthermore, a novel event-triggered impulsive control (ETIC) is designed to further reduce the communication bandwidth. By using linear matrix inequality (LMI) technique and constructing appropriate Lyapunov functions, some sufficient criteria guaranteeing the synchronization of the DTCNNs are obtained. Finally, We propose a simulation example to illustrate the validity and feasibility of the theoretical results obtained.

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This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types.

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This paper deals with the fuzzy filtering problem for a class of nonlinear time-delay systems described by T-S fuzzy models. Different from the existing schemes in the literature, this paper aims to solve the fuzzy filtering problem by considering the H∞, L2 - L∞ and dissipative performance constraints in a unified way. To achieve this purpose, the recently proposed notion of extended dissipativity is applied, which provides an inequality covering the well-known H∞, L2 - L∞ and dissipative performances. Another purpose of this paper is to design filters involving communication delays. Such filters have a more general form than the delay-free filters that have been largely considered in the traditional studies. In order to design the fuzzy filters under consideration, a novel fuzzy Lyapunov-Krasovskii functional is employed, and delay-dependent conditions for stability and performance analysis of the filtering error system are obtained. Then, LMI-based conditions for the existence of the desired filters are presented. The filter parameters can be obtained by solving the presented LMIs. Finally, the effectiveness of the proposed method is substantiated with an illustrative example.

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We present a mathematical model which describes the growth of malignant gliomas in presence of immune responses by considering the role of immunotherapeutic agent T11 target structure (T11TS). The model consider five populations, namely, glioma cells, macrophages, cytotoxic T-lymphocytes, TGF - ß and IFN - γ. The model system has highly nonlinear terms with four discrete time lags, but remains tractable. The goal of this work is to better understand the effect of multiple delays on the interaction between gliomas and immune components in conjunction with an administration of T11 target structure. Analytically, we investigate the conditions for the asymptotic stability of equilibrium points, the existence of Hopf bifurcations and the maximum value of the delay to preserve the stability of limit cycle. For the set of parameter values estimated from experimental data, time delays have hardly any influence on the system behavior. Numerical simulations are carried out to investigate the dynamics of the model with different values for delays with and without administration of T11 target structure.

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The paper presents theoretical results on the global asymptotic stability and synchronization of a class of fractional-order memristor-based neural networks (FMNN) with multiple delays. First, the asymptotic stability of fractional-order (FO) linear systems with single or multiple delays is discussed. Delay-independent stability criteria for the two types of systems are established by using the maximum modulus principle and the spectral radii of matrices. Second, new testable algebraic criteria for ensuring the existence and global asymptotic stability of the system equilibrium point are obtained by employing the Kakutani's fixed point theorem of set-valued maps, the comparison theorem, and the stability criterion for FO linear systems with multiple delays. Third, the synchronization criterion for FMNN is presented based on the linear error feedback control. Finally, numerical examples are given demonstrating the effectiveness of the proposed results.

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Time delay is an inevitable factor in neural networks due to the finite propagation velocity and switching speed. Neural system may lose its stability even for very small delay. In this paper, a two-neural network system with the different types of delays involved in self- and neighbor- connection has been investigated. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the multiple delays can lead the system dynamic behavior to exhibit stability switches. The delay-dependent stability regions are illustrated in the delay-parameter plane, followed which the double Hopf bifurcation points can be obtained from the intersection points of the first and second Hopf bifurcation, i.e., the corresponding characteristic equation has two pairs of imaginary eigenvalues. Taking the delays as the bifurcation parameters, the classification and bifurcation sets are obtained in terms of the central manifold reduction and normal form method. The dynamical behavior of system may exhibit the quasi-periodic solutions due to the Neimark- Sacker bifurcation. Finally, numerical simulations are made to verify the theoretical results.