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This paper addresses the state-dependent impulsive effects on robust exponential stability of quaternion-valued neural networks (QVNNs) with parametric uncertainties. In view of the noncommutativity of quaternion multiplication, we have to separate the concerned quaternion-valued models into four real-valued parts. Then, several assumptions ensuring every solution of the separated state-dependent impulsive neural networks intersects each of the discontinuous surface exactly once are proposed. In the meantime, by applying the $B$ -equivalent method, the addressed state-dependent impulsive models are reduced to fixed-time ones, and the latter can be regarded as the comparative systems of the former. For the subsequent analysis, we proposed a novel norm inequality of block matrix, which can be utilized to analyze the same stability properties of the separated state-dependent impulsive models and the reduced ones efficaciously. Afterward, several sufficient conditions are well presented to guarantee the robust exponential stability of the origin of the considered models; it is worth mentioning that two cases of addressed models are analyzed concretely, that is, models with exponential stable continuous subsystems and destabilizing impulses, and models with unstable continuous subsystems and stabilizing impulses. In addition, an application case corresponding to the stability problem of models with unstable continuous subsystems and stabilizing impulses for state-dependent impulse control to robust exponential synchronization of QVNNs is considered summarily. Finally, some numerical examples are proffered to illustrate the effectiveness and correctness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses the multistability issue for quaternion-valued neural networks (QVNNs) with time delays. By using the inequality technique, sufficient conditions are proposed for the boundedness and the global attractivity of delayed QVNNs. Based on the geometrical properties of the activation functions, several criteria are obtained to ensure the existence of $81^{n}$ equilibrium points, $16^{n}$ of which are locally stable. Two numerical examples are provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper presents new results on multistability of networks when neurons undergo self-excitation and second-order synaptic connectivity. Due to self-excitation of neurons, we split state space into invariant regions and establish new criteria of coexistence of equilibria (periodic orbits) which are exponentially stable. It is shown that high-order synaptic connectivity and external inputs play an important role on the number of equilibria and their convergent dynamics. As a consequence, our results refute traditional viewpoint: high-order interactions of neurons have faster convergence rate and greater storage capacity than first-order ones. Finally, numerical simulations will illustrate our new and interesting results. [ABSTRACT FROM PUBLISHER]