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Spruce budworm is a major defoliator of forests in North America and its periodic outbreak can cause severe economic growth loss. In 2008, Vaidya and Wu proposed a delayed spruce budworm population model and studied the impact of physiological structure on outbreak control (Vaidya and Wu, 2008 [27]). In this paper, we revisit this model and study its global dynamics that has not been analyzed previously. By carefully dealing with the major difficulty caused jointly by the time delay and the nonlinearity, we give a rather complete stability analysis for the model, including global asymptotic stability, bistability, semi-stability and Hopf bifurcation. Moreover, we show that the time delay can induce interesting dynamics including multitype bistability and long transients. [ABSTRACT FROM AUTHOR]

This paper presents a new asymmetric Lyapunov–Krasovskii functional method for investigating the asymptotic stability of time‐delay systems. Two resulting delay‐dependent asymptotic stability conditions in the form of linear matrix inequalities are given. The advantages of the new approaches are verified theoretically and numerically. [ABSTRACT FROM AUTHOR]

This paper analyses a mathematical model with time delay for the labor force on a market. Three variables are taken into account: the number of unemployed and employed persons in the market and the number of new vacancies created by the government and the private sector, which is based on a past value of the unemployment number in the creation of new vacancies. The positivity of the solutions is examined and the existence of a unique equilibrium point of the mathematical model is proved. A local stability analysis is undertaken, showing that the unique equilibrium is locally asymptotically stable, for any value of the time delay. Numerical simulations are carried out which substantiate the theoretical statements and suggest that the positive equilibrium point is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

This comment is to point out some mistakes made in the paper (Shiva et al in MATH METHOD APPL SCI 42(7):2302‐2323, 2019). The stability of Prabhakar fractional dynamical systems without and with time delay is addressed. Lyapunov stability theorem is extended to these systems. But the proof process is wrong as the memory property of fractional calculus. It is necessary to point out these errors to avoid misleading. Finally, a counterexample is proposed against the proposed theorem. [ABSTRACT FROM AUTHOR]

This paper addresses the stability issue of delayed switched nonlinear systems whose subsystem is of the form x ̇ ( t ) = A ( t , x ( t ) , x t − d ( t ) ) x ( t ) + B ( t , x ( t ) , x t − d ( t ) ) x t − d ( t ) , that is, the system matrices depend on time and the present and past states. By means of a trajectory-based comparison approach, stability of original switched nonlinear system is transformed into that of a switched positive linear system called a comparison system. The involved delays are piecewise continuous and may be unbounded. The comparison switched system may consist of unstable subsystems. It is shown that if the comparison system is asymptotically or exponentially stable, then the original system is asymptotically or exponentially stable, globally or locally, depending on the domain chosen to form the comparison system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the problem of delay-dependent stability analysis of time-varying delay systems is investigated. Firstly, a new inequality which is the modified version of free-matrix-based integral inequality is derived, and then by aid of this new inequality, two novel lemmas which are relaxed conditions for some matrices in a Lyapunov function are proposed. Based on the lemmas, improved delay-dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality (LMI). Two numerical examples are given to describe the less conservatism of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results. [ABSTRACT FROM AUTHOR]

Considering the ability of network users to distinguish and refute the rumor, we establish a Susceptible–Believed–Denied (SBD) rumor spreading model with nonlinear incidence rate and time delay in complex networks. Specifically, two dynamical systems of rumor propagation are given based on the mean field theory in homogeneous and heterogeneous networks respectively. Then, we obtain the equilibrium points of the systems and calculate the basic reproduction number R 0 according to the next generation matrix in homogeneous networks and the existence of a positive equilibrium point in heterogeneous networks. The local and global asymptotic stabilities of the rumor-free equilibrium points are demonstrated by constructing Lyapunov functions under the given condition R 1 ≤ 1. Further, we perform representative numerical simulations to illustrate the theoretical results. Through simulation experiments, the dynamics around the rumor-spreading equilibrium points when R 0 > 1 are also discussed to complement some dynamical properties of our models. • This paper presents a novel SBD rumor spreading model combined with classifying thought. • Comparative analysis of homogeneous and heterogeneous networks is numerically given. • Stability is proved in a strict mathematical way. [ABSTRACT FROM AUTHOR]

In most of the numerical examples of time-delay systems proposed in the literature, the number of unstable characteristic roots remains positive before and after a multiple critical imaginary root (CIR) appears (as the delay, seen as a parameter, increases). This fact may lead to some misunderstandings: (i) A multiple CIR may at most affect the instability degree; (ii) It cannot cause any stability reversals (stability transitions from instability to stability). As far as we know, whether the appearance of a multiple CIR can induce stability is still unclear (in fact, when a CIR generates a stability reversal has not been specifically investigated). In this paper, we provide a finer analysis of stability reversals and some new insights into the classification: the link between the multiplicity of a CIR and the asymptotic behavior with the stabilizing effect. Based on these results, we present an example illustrating that a multiple CIR's asymptotic behavior is able to cause a stability reversal. To the best of the authors' knowledge, such an example is a novelty in the literature on time-delay systems. [ABSTRACT FROM AUTHOR]