Cognitive and Neural Systems (CNS), to develop neuromorphic architectures which may be based on memristive systems. Memristive networks are a particular type of physical neural network that have very similar properties to (Little-)Hopfield networks, as they have a continuous dynamics, have a limited memory capacity and they natural relax via the minimization of a function which is asymptotic to the Ising model. In this sense, the dynamics of a memristive circuit has the advantage compared to a Resistor-Capacitor network to have a more interesting non-linear behavior. From this point of view, engineering an analog memristive networks accounts to a peculiar type of neuromorphic engineering in which the device behavior depends on the circuit wiring, or topology. The evolution of these networks can be studied analytically using variations of the Caravelli-Traversa-Di Ventra equation. Training Gradient descent Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. In neural networks, it can be used to minimize the error term by changing each weight in proportion to the derivative of the error with respect to that weight, provided the non-linear activation functions are differentiable. Various methods for doing so were developed in the 1980s and early 1990s by Werbos, Williams, Robinson, Schmidhuber, Hochreiter, Pearlmutter and others. The standard method is called "backpropagation through time" or BPTT, and is a generalization of back-propagation for feed-forward networks. Like that method, it is an instance of automatic differentiation in the reverse accumulation mode of Pontryagin's minimum principle. A more computationally expensive online variant is called "Real-Time Recurrent Learning" or RTRL, which is an instance of automatic differentiation in the forward accumulation mode with stacked tangent vectors. Unlike BPTT, this algorithm is local in time but not local in space. In this context, local in space means that a unit's weight vector can be updated using only information stored in the connected units and the unit itself such that update complexity of a single unit is linear in the dimensionality of the weight vector. Local in time means that the updates take place continually (on-line) and depend only on the most recent time step rather than on multiple time steps within a given time horizon as in BPTT. Biological neural networks appear to be local with respect to both time and space. For recursively computing the partial derivatives, RTRL has a time-complexity of O(number of hidden x number of weights) per time