The underlying graph of a deterministic synchronous dynamical system, where each node has a state value from {0, 1}, is shown in Figure 2. Assume that the system is progressive, i.e., once a node reaches state 1, it remains in that state. Each node has a threshold of 2, 2 neighbors need to be infected for a node to become infected. Suppose the system starts at time 0 m the configuration where nodes 1, 6 and 7 are in state 1 while the other nodes are in state 0. Note that a configuration specifies a state value for each node. For example, the configuration of the system when nodes 2 and 3 are in state 1 is (0, 1, 1, 0, 0, 0, 0). Show the successive configurations of the system until it reaches a fixed point. Find an initial configuration with the smallest number of nodes in state 1 such that the system reaches a fixed point where every node is in state 1. Indicate how you arrived at your solution. The underlying graph of a deterministic synchronous dynamical system, where each node has a state value from {0, 1}, is shown in Figure 2. Assume that the system is progressive, i.e., once a node reaches state 1, it remains in that state. Each node has a threshold of 2, 2 neighbors need to be infected for a node to become infected. Suppose the system starts at time 0 m the configuration where nodes 1, 6 and 7 are in state 1 while the other nodes are in state 0. Note that a configuration specifies a state value for each node. For example, the configuration of the system when nodes 2 and 3 are in state 1 is (0, 1, 1, 0, 0, 0, 0). Show the successive configurations of the system until it reaches a fixed point. Find an initial configuration with the smallest number of nodes in state 1 such that the system reaches a fixed point where every node is in state 1. Indicate how you arrived at your solution