Abstract: Previous studies suggested that lateral interactions of V1 cells are responsible, among other visual effects, of bottom-up visual attention (alternatively named visual salience or saliency). Our objective is to mimic these connections with a neurodynamic network of firing-rate neurons in order to predict visual attention. Early visual subcortical processes (i.e. retinal and thalamic) are functionally simulated. An implementation of the cortical magnification function is included to define the retinotopical projections towards V1, processing neuronal activity for each distinct view during scene observation. Novel computational definitions of top-down inhibition (in terms of inhibition of return, oculomotor and selection mechanisms), are also proposed to predict attention in Free-Viewing and Visual Search tasks. Results show that our model outpeforms other biologically inspired models of saliency prediction while predicting visual saccade sequences with the same model. We also show how temporal and spatial characteristics of saccade amplitude and inhibition of return can improve prediction of saccades, as well as how distinct search strategies (in terms of feature-selective or category-specific inhibition) can predict attention at distinct image contexts.