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In this study, a stability and stabilization analysis is discussed for Takagi–Sugeno (T-S) fuzzy systems with distributed time-delays. A fuzzy-based memory state-feedback control is designed to stabilize the delayed T-S fuzzy systems. A new Lyapunov–Krasovskii functional is constructed in an augmented form with information about the lower and upper bounds. Based on this functional, asymptotic stability of the closed-loop T-S fuzzy systems is achieved, and sufficient conditions are derived in linear matrix inequality form. In the numerical example section, comparative results are given with their simulation results to show the merits of the proposed approach and control scheme. • This study focuses on the stability problem of distributed delayed T-S fuzzy systems. • An augmented type of Lyapunov–Krasovskii functional is built with delay information. • A state-feedback controller is constructed to stabilize the delayed T-S fuzzy system. • Conservative results are obtained by employing GFWMA inequality. • Numerical examples provide the strength of this work compared with the existing work. [ABSTRACT FROM AUTHOR]

Macrophages are capable of producing large amounts of both intracellular and extracellular infected cells without necessarily succumbing to the lethal effects of productive viral infection. In this manuscript, authors studied the macrophages infection by human immunodeficiency virus type 1 in the form of mathematical models along with two different types of delays. The asymptotic stability of the constructed model without time delay is proved by utilizing the roots of the characteristic quasi-polynomial which is obtained by applying Jacobian matrix method. Based on Routh–Hurwitz criterion, the dynamical properties of model with a delay is investigated. Instead of discrete time delay, the effect of distribution of delays in the immune activation is also analyzed by using linear chain trick technique. In particular, the model undergoes Hopf bifurcation depending on the critical value of single delay in the activation of immune response. Anti-retroviral treatments have been used to control the replication of HIV-1 virus in infected patients is investigated along with time delay. Moreover, it is proved that the existence of two different types of delays may cause the solutions of the model to become stable or unstable depending on the conditions of chosen bifurcation parameter. Numerical simulations are performed to validate the derived theoretical results. [ABSTRACT FROM AUTHOR]

This brief is mainly concerned with a series of dynamical analyses of the Hindmarsh–Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov–Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This study addresses the master and slave synchronization problem of chaotic fractional-order delayed neural networks using a non-fragile sampled-data control (NFSDC) scheme which includes uncertainty information in the control gain matrix. An appropriate Lyapunov functional is constructed with information about sampling instants. A new, improved fractional-order inequality is developed to estimate the integral term. Then, based on the new integral inequality, the delay-dependent stability criteria are derived in the form of linear matrix inequality, which guarantees the asymptotic stability of the fractional-order error systems. This implies that the proposed NFSDC can synchronize the fractional-order master and slave systems. Moreover, numerical simulation results illustrate the synchronization nature and the influence of fractional derivatives in the system dynamics. Finally, it can be concluded that the proposed method and control scheme are effective. • For fractional-order neural networks, a non-fragile sampled data control is proposed. • A new lemma is derived for estimating the fractional derivative of integral terms. • Synchronization is attained for chaotic fractional-order master and slave systems. • The comparison result indicates that the proposed control scheme is effective. [ABSTRACT FROM AUTHOR]

Neutron star interiors provide the opportunity to probe properties of cold dense matter in the QCD phase diagram. Utilizing models of dense matter in accord with nuclear systematics at nuclear densities, we investigate the compatibility of deconfined quark cores with current observational constraints on the maximum mass and tidal deformability of neutron stars. We explore various methods of implementing the hadron-to-quark phase transition, specifically, first-order transitions with sharp (Maxwell construction) and soft (Gibbs construction) interfaces, and smooth crossover transitions. We find that within the models we apply, hadronic matter has to be stiff for a first-order phase transition and soft for a crossover transition. In both scenarios and for the equations of state we employed, quarks appear at the center of premerger neutron stars in the mass range ≈1.0-1.6  M⊙, with a squared speed of sound cQM²≳0.4 characteristic of strong repulsive interactions required to support the recently discovered neutron star masses ≥2  M⊙. We also identify equations of state and phase transition scenarios that are consistent with the bounds placed on tidal deformations of neutron stars in the recent binary merger event GW170817. We emphasize that distinguishing hybrid stars with quark cores from normal hadronic stars is very difficult from the knowledge of masses and radii alone, unless drastic sharp transitions induce distinctive disconnected hybrid branches in the mass-radius relation. [ABSTRACT FROM AUTHOR]