Impulsively synchronizing chaotic systems with delay and applications to secure communication

In this paper, the presence of transmission delay and sampling delay in chaos-based secure communication systems by employing impulsive synchronization is studied. A time delayed impulsive differential system with delayed impulses, modeling the synchronization error between the driving and response schemes employed in such communication systems, is presented. The equi-attractivity property of the error dynamics is investigated and the sufficient conditions leading to this property are obtained. A set of upper bounds on the delay terms involved in the system are also obtained, and a numerical example is given. A communication security scheme employing hyperchaotic systems possessing continuous driving, impulsive driving and delay is proposed and simulation results are given to demonstrate the performance of the scheme.

[1]  R. E. Amritkar,et al.  Synchronization of chaotic orbits: The effect of a finite time step. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Leon O. Chua,et al.  Conditions for impulsive Synchronization of Chaotic and hyperchaotic Systems , 2001, Int. J. Bifurc. Chaos.

[3]  S. Mascolo,et al.  Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal , 1997 .

[4]  Xinzhi Liu,et al.  Application of Impulsive Synchronization to Communication Security , 2003 .

[5]  V. Lakshmikantham,et al.  Stability Analysis in Terms of Two Measures , 1993 .

[6]  S. Mascolo,et al.  A system theory approach for designing cryptosystems based on hyperchaos , 1999 .

[7]  Xinzhi Liu,et al.  Existence, uniqueness and boundedness results for impulsive delay differential equations , 2000 .

[8]  L. Chua,et al.  Generalized synchronization of chaos via linear transformations , 1999 .

[9]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[10]  J. Suykens,et al.  Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback , 1998 .

[11]  Leon O. Chua,et al.  Spread Spectrum Communication Through Modulation of Chaos , 1993 .

[12]  Leon O. Chua,et al.  EXPERIMENTAL STUDY OF IMPULSIVE SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC CIRCUITS , 1999 .

[13]  Parlitz,et al.  Driving and synchronizing by chaotic impulses. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[15]  Saverio Mascolo,et al.  Synchronizing Hyperchaotic Systems by Observer Design , 1999 .

[16]  L. Chua,et al.  Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication , 1997 .

[17]  Alan V. Oppenheim,et al.  Chaotic signals and systems for communications , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[18]  L. Chua,et al.  Hyper chaos: Laboratory experiment and numerical confirmation , 1986 .

[19]  Leon O. Chua,et al.  Experimental Demonstration of Secure Communications via Chaotic Synchronization , 1992, Chua's Circuit.

[20]  Peng,et al.  Synchronizing hyperchaos with a scalar transmitted signal. , 1996, Physical review letters.

[21]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[22]  C. W. Chan,et al.  Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations , 2001 .

[23]  Y. Soh,et al.  The stabilization and synchronization of Chua's oscillators via impulsive control , 2001 .

[24]  G. Grassi,et al.  Synchronizing hyperchaotic systems by observer design , 1999 .