Crosstalk phenomena taking place between synapses can influence signal transmission and, in some cases, brain functions. It is thus important to discover the dynamic behaviors of the neural network infected by synaptic crosstalk. To achieve this, in this paper, a new circuit is structured to emulate the Coupled Hyperbolic Memristors, which is then utilized to simulate the synaptic crosstalk of a Hopfield Neural Network (HNN). Thereafter, the HNN's multi-stability, asymmetry attractors, and anti-monotonicity are observed with various crosstalk strengths. The dynamic behaviors of the HNN are presented using bifurcation diagrams, dynamic maps, and Lyapunov exponent spectrums, considering different levels of crosstalk strengths. Simulation results also reveal that different crosstalk strengths can lead to wide-ranging nonlinear behaviors in the HNN systems.In this paper, almost sure exponential stabilization and destabilization criteria for nonlinear systems are obtained via aperiodically intermittent stochastic noises based on average techniques and piecewise continuous scalar functions. Compared with existing results on almost sure exponential stability of stochastic systems, the requirement on the upper bound of the diffusion operator of a Lyapunov function is released. The upper bound is allowed to be a scalar function and even be unbounded. Simultaneously, by means of putting forward new concepts "average noise control rate" and "average noise control period," assumptions on infimum of control time and supremum of rest time in the previous references about aperiodically intermittent control can be removed without implementing in the upper limit of the uncontrolled rate, which reduces the conservativeness of stabilization criteria resulting from non-uniform distribution of control time and rest time. In addition, the main results are applied to coupled and uncoupled nonlinear spring-mass-damper oscillator systems, respectively, and corresponding numerical simulations are carried out to demonstrate the validity of the theoretical analysis.Extreme events appear in many complex nonlinear dynamical systems. Predicting extreme events has important scientific significance and large societal impacts.  https://www.selleckchem.com/products/bms-927711.html  In this paper, a new mathematical framework of building suitable nonlinear approximate models is developed, which aims at predicting both the observed and hidden extreme events in complex nonlinear dynamical systems for short-, medium-, and long-range forecasting using only short and partially observed training time series. Different from many ad hoc data-driven regression models, these new nonlinear models take into account physically motivated processes and physics constraints. They also allow efficient and accurate algorithms for parameter estimation, data assimilation, and prediction. Cheap stochastic parameterizations, judicious linear feedback control, and suitable noise inflation strategies are incorporated into the new nonlinear modeling framework, which provide accurate predictions of both the observed and hidden extreme events as well as the strongly non-Gaussian statistics in various highly intermittent nonlinear dyad and triad models, including the Lorenz 63 model. Then, a stochastic mode reduction strategy is applied to a 21-dimensional nonlinear paradigm model for topographic mean flow interaction. The resulting five-dimensional physics-constrained nonlinear approximate model is able to accurately predict extreme events and the regime switching between zonally blocked and unblocked flow patterns. Finally, incorporating judicious linear stochastic processes into a simple nonlinear approximate model succeeds in learning certain complicated nonlinear effects of a six-dimensional low-order Charney-DeVore model with strong chaotic and regime switching behavior. The simple nonlinear approximate model then allows accurate online state estimation and the short- and medium-range forecasting of extreme events.We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized with desynchronized states and periodic with aperiodic motions. We show symmetric patterns for which both populations have the same type of dynamics as well as chimera states of a broken symmetry. The network can furthermore show multistability by settling to distinct dynamics for different realizations of random initial conditions or by switching intermittently between distinct dynamics for the same realization. We conclude that our system of two populations of a particularly simple map is the most simple system that can show this highly diverse and complex behavior, which includes but is not limited to chimera states. As an outlook to future studies, we explore the stability of two populations of quadratic maps with a complex-valued control parameter. We show that bounded and diverging dynamics are separated by fractal boundaries in the complex plane of this control parameter.A chiral CpRhIII-catalyzed asymmetric C-H activation reaction of N-methoxybenzamides with quinones has been developed to efficiently forge chiral tricyclic hydrophenanthridinone scaffolds in ≤88% yield and ≤94% ee. With this methodology as the key step, an enantioenriched dihydrolycoricidine derivative has been synthesized in 64% overall yield in five steps.We describe a novel method to synthesize 2,5-dialkyl-4,6,7-tricyanoindole derivatives from a base-catalyzed reaction of 1,3-diketones with fumaronitrile. The reaction proceeds by the condensation of two molecules of fumaronitrile and one molecule of 1,3-diketone in a remarkable process that involves the cleavage of one C(sp3)-C(sp2) bond in 1,3-diketones and the formation of one carbon-nitrogen bond and four carbon-carbon bonds to construct both the aryl and pyrrole rings of the indole in one step.A rhodium-catalyzed [4 + 2 + 1] cycloaddition involving 1,3-diene, alkyne, and silylene to afford silicon-containing seven-membered rings was established. In the presence of a rhodium catalyst bearing bis(diphenylphosphino)methane (DPPM), nona-1,3-dien-8-yne derivatives reacted efficiently at 80-110 °C with boryl(isopropoxy)silane or boryl(diethyamino)silane, which reacts as the synthetic equivalent of silylene, to afford 1-silacyclohepta-2,5-dienes (2,5-dihydro-1H-silepines). Regiodivergent and chemo- and stereoselective functionalization of the seven-membered nonconjugated diene was achieved by hydroboration mediated by Cs2CO3 or an iridium catalyst.