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Our focus of this paper is on global Mittag-Leffler synchronization (GMLS) of the Caputotype Inertial Cohen-Grossberg Neural Networks (ICGNNs) with discrete and distributed delays. This model takes into account the inertial term as well as the two types of delays, which greatly reduces the conservatism with respect to the model. A change of variables transforms the 2β order inertial frame into β order ordinary frame in order to deal with the effect of the inertial term. In the following steps, two novel types of delay controllers are designed for the purpose of reaching the GMLS. In conjunction with the novel controllers, utilizing differential mean-value theorem and inequality techniques, several criteria are derived to determine the GMLS of ICGNNs within the framework of Caputo-type derivative and calculus properties. At length, the feasibility of the results is further demonstrated by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper presents the first investigation of extended dissipative synchronization in a specific type of Takagi-Sugeno (T-S) fuzzy complex dynamical networks with interval hybrid coupling delays. First, the decoupling method is employed to reorganize the multiple communication dynamical system, which comprises discrete-time, partial and distributed coupling delays. Second, the non-fragile control, which allows for uncertainty management within predefined norm bounds, has been applied to networks. Moreover, it becomes possible to derive a less conservative condition by utilizing multiple integral Lyapunov functionals, a decoupling strategy, Jensen's inequality, Wirtinger's inequality, and mathematical inequality techniques. This condition ensures that the T-S fuzzy complex dynamical networks, with interval hybrid coupling delays, can attain asymptotic synchronization with the assistance of a non-fragile feedback controller. Additionally, we extended this system to the extended dissipativity analysis, including passivity, L2 - L∞, H∞ and dissipativity performance in a unified formulation. A set of strict linear matrix inequalities (LMIs) conditions is a sufficient criterion. Finally, two simulation examples are proposed to verify the merit of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of octonion-valued neural networks with leakage delays and mixed delays. Considering that the multiplication of octonion algebras does not satisfy the associativity and commutativity, we can obtain the existence and global exponential stability of weighted pseudo almost periodic solutions for octonion-valued neural networks with leakage delays and mixed delays by using the Banach fixed point theorem, the proof by contradiction and the non-decomposition method. Finally, we will give one example to illustrate the feasibility and effectiveness of the main results. [ABSTRACT FROM AUTHOR]

In this work, the following stochastic Rayleigh-Stokes equations are considered ∂t[x(t) + f(t, xρ(t))] = (A + ...∂tβ A) [x(t) + f(t, xρ(t))] + g(t, xΤ (t)) + B(t, xξ(t)) ... (t), which involve the Riemann-Liouville fractional derivative in time, delays and standard Brownian motion. Under two different conditions for the non-linear external forcing terms, two existence and uniqueness results for the mild solution are established respectively, in the continuous space C([-h, T]; Lp(Ω, Vq)), p ≥ 2, q ≥ 0. Our study was motivated and inspired by a series of papers by T. Caraballo and his colleagues on stochastic differential equations containing delays. [ABSTRACT FROM AUTHOR]

Recent studies have shown that, in addition to direct predation, fear of predators alters the physiological behavior of prey. Based on this fact, this paper investigates a three-species food chain based on ratio-dependent and Beddington-DeAngelis type functional responses, which incorporates fear effects and two gestation delays. The positivity, boundedness and existence of equilibrium points of the system are investigated, and the local stability behavior of the equilibrium points and the occurrence of Hopf-bifurcation when the time lag parameters exceed the critical values are studied by analyzing the corresponding characteristic equations. The main results show that Hopf-bifurcation occurs when the time delay parameters attain the thresholds. Finally, numerical simulations are performed to verify our main results. [ABSTRACT FROM AUTHOR]

The general delay Hopfield neural network is studied. It is considered the case of time-varying delay, continuously distributed delays, time varying coefficients and a special type of a Riemann-Liouville fractional derivative (GPRLFD) with an exponential kernel. The presence of delays and GPRLFD in the model require two special types of initial conditions. The applied GPRLFD also required a special definition of the equilibrium of the model. A constant equilibrium of the model is defined. We use Razumikhin method and Lyapunov functions to study stability properties of the equilibrium of the model. We apply Lyapunov functions defined by absolute values as well as quadratic Lyapunov functions. We prove some comparison results for Lyapunov function connected deeply with the applied GPRLFD and use them to obtain exponential bounds of the solutions. These bounds are satisfied for intervals excluding the initial time. Also, the convergence of any solution of the model to the equilibrium at infinity is proved. An example illustrating the importance of our theoretical results is also included. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weakly damped wave equations with hereditary effects and the nonlinearity ff satisfying sup-cubic growth. Based on the recent extension of the Strichartz estimates to the case of bounded domains, we establish the global well-posedness of the Shatah-Struwe solutions for the non-autonomous case. Then, we prove the existence of the pullback D-attractors in CH10(Ω) × CL2(Ω) for the solutions process {U(t,τ)}t≥τ by applying the idea of contractive functions. [ABSTRACT FROM AUTHOR]

The 2-dimensional system of neutral type nonlinear difference equations with delays in the following form ... is considered. In this paper we use Schauder's fixed point theorem to study the existence of periodic solutions of the above system. [ABSTRACT FROM AUTHOR]

We establish a class of intermittent bidirectional dispersal popula- tion models with almost periodic parameters and dispersal delays between two patches. The form of dispersal discussed in this paper is different from both continuous and impulsive dispersals, in which the dispersal behavior occurs either in a sustained manner or instantaneously; instead, it is a synthesis of these types. Dynamical properties such as permanence, existence, uniqueness, and globally asymptotic stability of almost periodic solutions are investigated by using Liapunov-Razumikhin type technique, using the comparison theorem, constructing a suitable Lyapunov functional, using almost periodic functional hull theory and analysis approach, etc. Finally, numerical simulations are presented and discussed to illustrate our analytic results, by which we find that intermittent dispersal systems are more complicated than continuous or impulsive dispersal systems. [ABSTRACT FROM AUTHOR]