Variables are not fixed at steady state level

Dear all, I have a consultation, I have a model for an open economy, with a production function with three inputs (labor, capital, and a composite good). The composite good is a combination of inputs that could be imported and combined with labor. I assume that there are two types of investment, investment in physical capital, the normal thing that we all know, and one type of investment that would be the imported good of the composite product.
My idea is to do a simulation, perfect foresight, in which everyone anticipates that the prices of the imported good would fall, and this should increase the investment of this good. My problem is that when I make the simulations the movements are very abrupt, even if I don’t make any changes and I make the simulation with the initial variables.
But my main question, if I don’t assume any trajectory, nor any change, the variables should be fixed at the initial level (they are values of the stationary state put by hand), and not vary, I attach a graph with some variables graph1.pdf (13.2 KB) , my impression is that some variable may have a unitary root, does anybody know how I can make that when making the simulation the variables do not vary and remain fixed in their stationary state?

There must be a mistake in your codes. If you start at a steady state, even if there is a unit root, the model will remain in that state without shocks.