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A new general hybrid neural networks with inertial term and mixed time-varying delays are proposed here by using the memristors connections. Then by building appropriate Lyapunov functionals and inequality technique, some new conditions assuring the global exponential stability of the hybrid neural networks are derived. The circuit implementation of the proposed hybrid neural networks are also presented here. In addition, the new proposed results here enrich and extend the earlier publications on neural networks. Lastly, numerical simulations show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

• A class of neurodynamic model with fuzziness, inertial terms, discontinuous feedback functions and distributed delays is proposed. • The fixed-time synchronization and predefined-time synchronization results for proposed delayed drive-response inertial neural networks are established directly without variables substitution method. • Two new effective feedback controllers were, respectively, designed to get new criteria on fixed-time synchronization and predefined-time synchronization of drive-response inertial neural networks with distributed delays. • The predefined-time synchronization criteria for the proposed neurodynamic model are established in this paper, which convergence rate is more faster and settling time do not depend on initial values of drive response systems. This paper focuses on the fixed/predefined-time synchronization control of drive-response fuzzy inertial discontinuous neural networks(FIDNNs) with distributed delays. By using non-smooth analysis, fixed/predefined-time stability lemmas and designing two new fixed/predefined-time feedback controllers, several novel results are given to get fixed-time synchronization(FTS) and predefined-time synchronization(PTS) for the proposed FIDNNs. The fixed/predefined-time results of this paper are derived directly from FIDNNs themselves without variables substitution method. Up until now, very few results are reported on non-reduced order approach to achieve FTS and PTS of FIDNNs with distributed delays. Finally, some simulations and applications are, respectively, carried out to expound the efficacy of the obtained new FTS and PTS criteria. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to discuss the neutral predator–prey model with Hassell–Varley type functional response and two time-varying delays. Some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem. Finally, numerical simulations are then carried out as supporting evidences of our analytical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a differential–algebraic biological economic system with time delay and harvesting where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the differential–algebraic biological economic system based on the normal form approach and the center manifold theory. At last, numerical simulations are performed to illustrate the analytical results. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the stability and Hopf bifurcation of the biological economic system based on the new normal form and the Hopf bifurcation theorem. The basic model we consider is owed to a ratio-dependent predator–prey system with harvesting, compared with other researches on dynamics of predator–prey population, this system is described by differential-algebraic equations due to economic factor. Here μ as bifurcation parameter, it is found that periodic solutions arise from stable stationary states when the parameter μ increases close to a certain limit. Finally, numerical simulations illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

• In this paper, the p-norm fixed-time synchronization of delayed ICVNNs is investigated for the first time, in which the settling time estimation in terms of p-norm is derived. Our results are more flexible and adjustable than these results [36–38]. • Compared with the works [3,13,36-38,42], what we get herein is fixed-time synchronization, and these results are also applied to image encryption. • Different from the real-valued INNs [5–7,19,21] and first-order CVNNs [13,39-42]. In this paper, the neural model is defined in the complex field and has an inertial term, which broadens the application range of INNs and makes up for some previous literature results. This paper researches the problem of p-norm fixed-time synchronization for a class of delayed inertial complex-valued neural networks (ICVNNs). By using reduced-order transformation and separating real and imaginary parts of complex-valued parameters , the second-order ICVNNs can be converted into the form of first-order real-valued differential equations. Then some new flexible and adjustable algebraic criteria to ensure the fixed-time synchronization of ICVNNs are established by means of the non-smooth Lyapunov function and inequality analytical techniques. Moreover, the settling time of fixed-time synchronization is theoretically estimated, which does not depend on the initial value of systems. Finally, simulation examples and applications are presented to illustrate the validity and availability of the obtained results. [ABSTRACT FROM AUTHOR]

The finite-time stabilization of discontinuous switched systems is a highly challenging problem. To address this problem, this article proposes a unified controller that achieves fixed-time and preassigned-time stabilization of discontinuous switched systems with time-varying delays, which is superior to finite-time stabilization. Compared with finite-time stabilization results, the settling time for fixed-time stabilization is independent of the initial state of the system. For preassigned-time stabilization, the settling time can be set in advance regardless of the initial state and controller parameters. Also, the fixed-time and preassigned-time stabilization methods proposed in this article are general and can be extended for applications to other nonlinear discontinuous systems with time delays. • A unified control framework is proposed to achieve both fixed-time and preassigned-time stabilization. • Achieve fixed-time stabilization of discontinuous switched systems and obtain more accurate settling times. • Different from finite-time stabilization, the settling time for fixed-time stabilization is independent of the initial state. • The settling time for preassigned-time stabilization can be set ready despite the initial state and controller parameters. [ABSTRACT FROM AUTHOR]