We report on the development of TiOx-based memristive devices for bio-inspired neuromorphic systems. In particular, capacitor like structures of Al/AlOx/TiOx/Al with, respectively 20 nm and 50 nm thick TiOx-layers were fabricated and analyzed in terms of their use in neural network circuits. Therefore, an equivalent circuit model is presented which mimics the observed device properties on a qualitative level and relies on mobile oxygen ions by taking electronic transport through local conducting filaments and hopping between TiOx defect states into account. The model also comprises back diffusion of oxygen ions and allows for a realistic description of the experimental recorded device characteristics. The in Refs. [1-3] reported computing paradigms for pattern recognition have been used as guidelines for a device performance investigation at the network level. In particular, simulations of a spiking neural network are presented which allows for pattern recognition. As input patterns hand written digits taken from the MNIST Data base have been used. Within the network the memristive devices are arranged in a cross-bar array connected by 196 input neurons and ten output neurons. While, each input neuron corresponds to a specific pixel of the image of the input pattern, the output neurons were implemented as spiking neurons. In addition, the output neurons were inhibitory linked within an winner-take-it-all network and consist of a homeostasis-like behavior for their spiking thresholds. Based on the network simulation essential requirements for the development of optimal memristive device for neuromorphic circuits are discussed.