Stability and Hopf bifurcation analysis of fractional-order complex-valued neural networks with time delays

Abstract This paper considers a class of fractional-order complex-valued Hopfield neural networks (CVHNNs) with time delay for analyzing the dynamic behaviors such as local asymptotic stability and Hopf bifurcation. In the case of a neural network with hub and ring structure, the stability of the equilibrium state is investigated by analyzing the eigenvalue of the corresponding characteristic matrix for the hub and ring structured fractional-order time delay models using a Laplace transformation for the Caputo-fractional derivatives. Some sufficient conditions are established to guarantee the uniqueness of the equilibrium point. In addition, conditions for the occurrence of a Hopf bifurcation are also presented. Finally, numerical examples are given to demonstrate the effectiveness of the derived results

Loss of GluN2B-containing NMDA receptors in CA1 hippocampus and cortex impairs long-term depression, reduces dendritic spine density, and disrupts learning

NMDA receptors (NMDARs) are key mediators of certain forms of synaptic plasticity and learning. NMDAR complexes are heteromers composed of an obligatory GluN1 subunit and one or more GluN2 (GluN2A-GluN2D) subunits. Different subunits confer distinct physiological and molecular properties to NMDARs, but their contribution to synaptic plasticity and learning in the adult brain remains uncertain. Here, we generated mice lacking GluN2B in pyramidal neurons of cortex and CA1 subregion of hippocampus. We found that hippocampal principal neurons of adult GluN2B mutants had faster decaying NMDAR-mediated EPSCs than nonmutant controls and were insensitive to GluN2B but not NMDAR antagonism. A subsaturating form of hippocampal long-term potentiation (LTP) was impaired in the mutants, whereas a saturating form of LTP was intact. An NMDAR-dependent form of long-term depression (LTD) produced by low-frequency stimulation combined with glutamate transporter inhibition was abolished in the mutants. Additionally, mutants exhibited decreased dendritic spine density in CA1 hippocampal neurons compared with controls. On multiple assays for corticohippocampal-mediated learning and memory (hidden platform Morris water maze, T-maze spontaneous alternation, and pavlovian trace fear conditioning), mutants were impaired. These data further demonstrate the importance of GluN2B for synaptic plasticity in the adult hippocampus and suggest a particularly critical role in LTD, at least the form studied here. The finding that loss of GluN2B was sufficient to cause learning deficits illustrates the contribution of GluN2B-mediated forms of plasticity to memory formation, with implications for elucidating NMDAR-related dysfunction in disease-related cognitive impairmen