Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems

Figure 8

(a) The behaviour of the trajectories 𝑒_𝑥, 𝑒_𝑦, 𝑒_𝑧 and 𝑒_𝑤 of the error system between hyperchaotic Lorenz system and hyperchaotic Chen system for anti-synchronization. (b): Show the estimates 𝛼₁(𝑡), 𝛽₁(𝑡), 𝛾₁(𝑡), 𝑟₁(𝑡) of the unknown parameters converges to 𝛼=10,𝛽=28,𝛾=8/3 and 𝑟=0.1as 𝑡 tends to 3. (c): Show the estimates 𝑎₁(𝑡), 𝑏₁(𝑡), 𝑐₁(𝑡), 𝑑₁(𝑡), 𝑙₁(𝑡) of the unknown parameters converges to 𝑎=35,𝑏=3,𝑐=12,𝑑=7 and 𝑙=0.5 as 𝑡 tends to 3.

(a)

(b)

(c)