[en] In this work, a flux-controlled memristor model with the state variable covering negative and positive states and having decay behavior is developed to link the plastic synapse and nonlinear spiking neuron. For the voltage dependence of the conductance, the trace-based voltage can be directly applied to the memristor without additional threshold to implement various synaptic plasticity such as STDP, anti-STDP, et al. At the same time, the memristor model can be introduced as adaption element in nonlinear models to reduce the model complexity while remaining the richness of firing patterns. A 2D nonlinear voltage-stimulated spiking neuron model with a memristor connecting to the input is developed. Stereotypically arranging the input voltages, various firing patterns observed in cortical neurons, such the tonic, adapting, burst, latency, and bistability, are successfully carried out in the neuron model. The flux-controlled memristor model can describe the electrical behavior of paired memristors with a power supply, and well link plastic synapses and nonlinear spiking neurons, which may be helpful for simulating and constructing a complex memristor-based neuromorphic system. (paper)