In this work, the behavior of two different systems, namely Lorenz and Chua, was studied and they were coupling together with a coupling factor *k* and the effect of this coupling on the behavior of the Lorenz system was studied.

The Lorenz system is defined by three ordinary differential equations, as follows[1]:

d/dt (*x*1) = σ (*y*1 – *x*1)

d/dt (*y*1) = (*x*1)(r- *z*1) – *y*1 (1)

d/dt (*z*1) = (*x*1)(*y*1) – β(*z*1)

Where the Lorenz parameters system [r, σ, and β] are real positive number that equal [28, 15, 2.1] respectively and the system exhibt chaotic behavior for these value. The initial conditions of the Lorenz system [*xi*1, *yi*1, *zi*1] were chosen to be [0, 0.1, 0], respectively.

For the Chua system, its electronic circuit can be analyzed using Kirchhoff's laws. The dynamics of an electronic circuit can be modeled with three nonlinear ordinary differential equations in the variables *x*, *y*, and *z*, as follows [2].

d/dt (*x*2) = *a*(*y*2 – *x*2 - g)

d/dt (*y*2) = *x*2 – *y*2 + *z*2 (2)

d/dt (*z*2) = -*b*(*y*2) + γ(*z*2)

g = c(*x*2) + (0.5)((*d* - *c*)(abs(*x*2 + 1) - abs(*x*2 − 1)))

Where Chua parameters system are [*a*, *b*, *c*, *d*, and γ] equal [15, 25.58, -0.714286, -1.14287, and 0.001] respectively and initial conditions [xi2, yi2, zi2] are [0, 0.1, 0] respectively.

To achieve complete synchronization between the Lorenz system and the Chua system, the coupling terms are added to all the equations of the Lorenz system, as shown below:

d/dt (*x*1) = σ (*y*1 – *x*1) + k(*x*2-*x*1)

d/dt (*y*1) = (*x*1)(r- *z*1) – *y*1 + k(*y*2-*y*1) (3)

d/dt (*z*1) = (*x*1)(*y*1) – β(*z*1) + k(*z*2-*z*1)

Where k(*x*2-*x*1), k(*y*2-*y*1), and k(*z*2-*z*1) are coupling terms and k is called coupling factor and is real numbers.