Corrigendum: Cascading failures in coupled networks with both inner-dependency and inter-dependency links

This Article contains typographical errors. In the Results section under subheading 'Scale-free networks' , " We keep R B constant in eq. (4), and check the behaviours of the order parameter R A " should read: " We keep R B constant in eq. (3), and check the behaviours of the order parameter R A " In the same section, " Similar to the coupled random networks, β ′ C and R B 0 can be solved numerically by letting = R 0 C A in eq. (4), " should read: " Similar to the coupled random networks, β ′ C and R B 0 can be solved numerically by letting = R 0 C A in eq. (3), " In the same section, " At the other tricritical point β c , the conditions of continuous and discontinuous percolation transitions are satisfied simultaneously, i.e., β c makes the first and the second order derivative of eq. (4) with respective S A hold at the percolation transition point p c ". should read: " At the other tricritical point β c , the conditions of continuous and discontinuous percolation transitions are satisfied simultaneously, i.e., β c makes the first and the second order derivative of eq. (3) with respective R A hold at the percolation transition point p c ". In the same section, " Similar to random networks, we cannot get the analytical expressions for the first order percolation transition points, but they can be solved numerically by eq. (4) ". should read: " Similar to random networks, we cannot get the analytical expressions for the first order percolation transition points, but they can be solved numerically by eqs. (3) and (4) " .