Chaos is one of the most significant topics in nonlinear
science, and has been intensively studying since the Lorenz
system [1] was introduced. After many chaotic systems has been
discovered and developed, scientists have focused on chaos
control and chaos synchronization since 1990s. Chaos
synchronization was discovered by Pecora and Carroll [2] and
there has been great interest in it, and its applications, such as
secure communication, and system identification. Given a
chaotic system considered as a master system, and another
identical system considered as a slave system, the dynamical
behaviors of them may be identical after a transient when the
slave system is driven by a control input. By using this
synchronization principle, some chaotic circuits were developed
and applied to secure communication systems [2-5].
Many methods have been developed to synchronize chaotic
systems, including nonlinear feedback method [6], adaptive
control method [7], anti-synchronization method [8] and sliding
mode control method [9]. Chaos synchronization using active
control which is introduced in [10] is one of the these methods.
Unified chaotic systems [11], the energy resource chaotic
system [12] and some other systems have been synchronized
with this method. Two identical systems are usually
synchronized by using of the methods mentioned above;
however, it is not always possible to assume that all components
are identical in engineering. Therefore, achieving
synchronization of two different chaotic systems is more
attractive and significant from a practical viewpoint.
The paper investigates the mathematical and practical
possibilities of synchronization of completely different chaotic
systems using active control. To this end, a mathematical model
is provided to solve synchronization problem of completely
different chaotic systems using active control in Section 2. In
Section 3, numerical simulations are provided to illustrate our
findings using the Lorenz system (which can be encountered in
atmospheric sciences, laser devices, and some other systems
related to convective heat transfer) as the master system, and the
Rössler system [13] (which can be encountered in chemical
reactions) as the slave system. Main conclusions to be drawn
from this study are given in Section 4.