  In this work we consider the effects of memory and bias in kinetic exchange
opinion models. We propose a model in which agents remember the sign of their
last interaction with each one of their pairs. This introduces memory effects
in the model, since past interactions can affect future ones. We have also
considered the impact of a parameter $p$ that regulates how often an agent
changes its interaction to match its opinion, thus introducing bias in the
interactions. For high values of $p$ an agent is more likely to start having a
negative interaction with an agent of opposing opinion and a positive
interaction with an agent of the same opinion. The model is defined on the top
of random networks with mean connectivity $\langle k \rangle$. We analyze the
impact of both $p$ and $\langle k \rangle$ on the emergence of ordered and
disordered states in the population. Our results suggest a rich phenomenology
regarding critical phenomena, with the presence of metastable states and a
non-monotonic behavior of the order parameter. We show that the fraction of
neutral agents in the disordered state decreases as the bias $p$ increases.
