Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems

Figure 7

(a) The behavior 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 complete synchronization. (b) the estimates 𝛼₁(𝑡), 𝛽₁(𝑡), 𝛾₁(𝑡), 𝑟₁(𝑡) of the unknown parameters converge to 𝛼=10,𝛽=28,𝛾=8/3, and 𝑟=0.1as 𝑡 tends to 3. (c) 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)