Figure 1

Example 1; The behavior of local fractional entropy for functions \(Q(\tau _{1})\) in the horizontal axis and \(Q(\tau _{2})\) in the vertical axis. Here, we suppose \(\alpha = 0.95\), \(C(i) = 0.499< 0.5\), \(i =1,2\), and \(A(i) = 0.1\), \(B(i) = 0.3\). This shows that the entropy solution is a unique solution for the system (6). Moreover, the equilibrium point is at the origin \((0,0)\). Note that when \(\alpha \to 0\), the system will loss its equilibrium