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The models of competitive neural network (CNN) was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications, where there are two types of memories: Long-term memories (LTM) and short-term memories (STM), LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity. This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator. By employing the appropriate differential inequality theory, some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector. Finally, an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.

This article examines the existence of the unique piecewise pseudo almost periodic for impulsive fuzzy cellular neural networks by using the contraction mapping principle and piecewise pseudo almost periodic function theory. Further, sufficient certain conditions for their global exponential stability are produced through the use of differential inequality and generalized Gronwall–Bellman inequality. Our results are new and complement some previously known ones. Two examples and their numerical simulations are performed to ensure our theoretical results.

In this paper, the exponential stability of piecewise pseudo almost periodic solutions for neutral-type inertial neural networks with time-varying, infinite-time distributed delays (mixed delays) and impulses are investigated. First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as the first-order differential equation. Second, by using inequality techniques and Lyapunov method, some sufficient conditions which ensure the existence and exponential stability of piecewise pseudo almost periodic solutions of inertial neural networks are presented. Finally, an example with graphical illustration is given to illustrate the effectiveness of the theoretical results.

This paper is concerned with a class of neutral type recurrent neural networks with time-varying delays, distributed delay and D operator on time–space scales which unify the continuous-time and the discrete-time recurrent neural networks under the same framework. Some sufficient conditions are given for the existence and the global exponential stability of the pseudo almost periodic solution by using inequality analysis techniques on time scales, fixed point theorem and the theory of calculus on time scales. An example is given to show the effectiveness of the derived results via computer simulations.

In this letter, the existence and the global exponential stability of piecewise pseudo almost periodic solutions (PAPT) for bidirectional associative memory neural networks (BAMNNs) with time-varying delay in leakage (or forgetting) terms and impulsive are investigated by applying contraction mapping fixed point theorem, the exponential dichotomy of linear differential equations and differential inequality techniques. Furthermore, we give an explanatory example to illustrate the efficiency of the theoretical predictions.

In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are taken into account. As an extension of the real-valued neural network, the Clifford-valued neural network, which includes a familiar complex-valued neural network and a quaternion-valued neural network as special cases, has been an active research field recently. By utilizing this novel method, which incorporates the differential inequality techniques and the fixed point theorem and time-scale theory of computation, we derive a few sufficient conditions to ensure the existence, uniqueness, and exponential stability of the pseudo almost periodic () solution of the considered model. The results in this paper are new, even if time scale $\mathbb{T}=\mathbb{R}$ T = R or $\mathbb{T}=\mathbb{Z}$ T = Z , and complementary to the previously existing works. Furthermore, an example and its numerical simulations are included to demonstrate the validity and advantage of the obtained results.

In this paper, Clifford-valued inertial neutral neural networks with time-varying delays and infinite distributed delay are investigated. With the help of the pseudo almost periodic function theory, Banach’s fixed point theorem, and the differential inequality theory, a set of sufficient criteria that guarantee the existence and the global exponential stability of unique pseudo-almost periodic solutions of Clifford-valued inertial neutral neural networks with mixed delays are established. Our results are new and complement some previously known ones. Moreover, numerical simulations are carried out to verify our theoretical results.

In this paper, bidirectional associative memory (BAM) neural networks with time-varying delays in leakage terms are investigated. A set of sufficient conditions are obtained for the existence and the exponential stability of pseudo almost periodic solutions for this class of neural networks by applying Banach’s fixed point theorems, and differential inequality techniques. Finally, we present a numerical example and simulation to illustrate the effectiveness of the theoretical results. We extend and improve previously know results.

The title compound, C12H19N2+·Cl−·H2O, contains a network of 4-(2,3-dimethylphenyl)piperazin-1-ium cations, water molecules and chloride anions. The crystal packing is influenced by O—H...Cl, N—H...Cl, N—H...O, C—H...O and C—H...Cl hydrogen bonds, resulting in structure with an open-framework architecture.

In the crystal structure of the title compound, (C10H15ClN2)[ZnCl4]·H2O, the Zn atom is coordinated by four Cl atoms in a tetrahedral geometry. The water molecules and the 1-(4-chlorophenyl)piperazine-1,4-diium cations interact with the [ZnCl4]2− anions through O—H...Cl, N—H...Cl, N—H...O and C—H...Cl hydrogen bonds (five simple and one bifurcated). Intermolecular π–π stacking interactions are present between adjacent aromatic rings of 1-(4-chlorophenyl)piperazine-1,4-diium cations (the centroid–centroid distance is 3.453 Å).

In the title compound, (C(4)H(12)N(2))[CdCl(4)]·H(2)O, the [CdCl(4)](2-) anions adopt a slightly distorted tetra-hedral configuration. In the crystal, O-H⋯Cl hydrogen bonds link the anions and water mol-ecules into corrugated inorganic chains along the b axis which are inter-connected via piperazinediiumN-H⋯O and N-H⋯Cl inter-actions into a three-dimensional framework structure.