Secure communications via modified complex phase synchronization of two hyperchaotic complex models with identical linear structure and adjusting in nonlinear terms

Abstract

We present a novel modified complex phase synchronization (MCPS) focusing on two hyperchaotic complex systems, including a comparative structure of direct terms with absolutely differing or not completely in nonlinear terms. We have used the active control theory for analytical control limits to achieve MCPS. It is shown that MCPS contains two sorts of synchronizations (phase and anti-phase synchronizations) and the state variables of the master system synchronize with substitute state components of the slave system. Numerical results are portrayed out to reveal the phases and modules errors of these hyperchaotic complex attractors, where the complex systems appear in various basic fields of material science and building. Also, we found that MCPS of the hyperchaotic complex structure synchronizes with another state variable of the slave structure is an empowering sort of synchronization as it contributes fabulous security in secure communication. In this secure communication, synchronization amongst transmitter and collector is closed and message signals are recovered. The encryption and recovery of the signals are imitated numerically.

Keywords

Complex synchronization hyperchaotic Stability theorem complex phase module

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References

Boccaletti ,

Kurths ,

Osipov ,

D.L.

Valladares and

C.S.

Zhou , The synchronization of chaotic systems, Phys Rep366 (2002), 1–101.

L.M.

Pecora and

T.L.

Carroll , Synchronization in chaotic frameworks, Phys Rev Lett64 (1990), 821–830.

G.M.

Mahmoud and

E.E.

Mahmoud , Complete synchronization of chaotic complex nonlinear frameworks with uncertain parameters, Nonlinear Dyn62 (2010), 875–882.

G.M.

Mahmoud and

E.E.

Mahmoud , Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear frameworks, Nonlinear Dyn61 (2010), 141–152.

Juan and

Xing-yuan , Nonlinear observer based phase synchronization of chaotic frameworks, Phys Lett A369 (2007), 294–298.

Liu , Anti-phase synchronization in coupled chaotic oscillators, Phys Rev E73 (2006), 057203.

A.E.

Hramov and

A.A.

Koronovskii , Generalized synchronization onset, Europhys Lett6 (2005), 01–907.

G.M.

Mahmoud and

E.E.

Mahmoud , Synchronization and control of hyperchaotic complex Lorenz system, Mathematics and Computers in Simulation80 (2010), 2286–2296.

G.H.

Li , Modified projective synchronization of chaotic framework, Chaos Solitons Fractals32 (2007), 1786–1790.

10.

Li ,

Liao and

Wong , Lag synchronization of hyperchaos with application to secure communications, Chaos, Solitons & Fractals23 (2005), 183–193.

11.

E.E.

Mahmoud , Modified projective phase synchronization of chaotic complex nonlinear systems, Math Comput Simul89 (2013), 69–85.

12.

G.M.

Mahmoud ,

E.E.

Mahmoud and

A.A.

Arafa , Projective synchronization for coupled partially linear complex-variable frameworks with known parameters, Math Meth Appl Sci40 (2017), 1214–1222.

13.

E.E.

Mahmoud and

M.A.

AL-Adwani , Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms, Results in Physics7 (2017), 1346–1356.

14.

Anischenko ,

Vadivasova ,

Postnov and

Safanova , Synchronization of chaos, Int J Bifur Chaos2 (1992), 633–644.

15.

Rosa Jr ,

W.B.

Pardo ,

C.M.

Ticos ,

J.A.

Walkenstein and

Monti , Phase synchronization of chaos in a plasma discharge tube, Int J Bifur Chaos10 (2000), 2551–2563.

16.

Tallon-Baudry ,

Bertrand ,

Delpuech and

Pernier , Stimulus specificity of phase-locked and non-phase-locked 40 Hz visual responses in human, Journal of Neuroscience16 (1996), 4240–4249.

17.

Wang ,

I.Z.

Kiss and

J.L.

Hudson , Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering, Chaos10 (2000), 248–256.

18.

Dabrowski ,

Galias and

Ogorzalek , Observations of phase synchronization phenomena in one-dimensional arrays of coupled chaotic electronic circuits, Int J Bifurc and Chaos10 (2000), 2391–2398.

19.

L.Y.

Cao and

Y.C.

Lai , Antiphase synchronism in chaotic frameworks, Phys Rev E58 (1998), 382–386.

20.

Jiang ,

Liu ,

Zhang and

Yu , Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators, Communications in Nonlinear Science and Numerical Simulation39 (2016), 199–208.

21.

E.E.

Mahmoud , An unusual kind of complex synchronizations and its applications in secure, Eur Phys J Plus132 (2017), 466.

22.

E.E.

Mahmoud , Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear frameworks, Math Methods App Sci37 (2014), 321–328.

23.

E.E.

Mahmoud and

K.M.

Abualnaja , Complex lag synchronization of two identical chaotic complex nonlinear frameworks, Cent Eur J Phys12 (2014), 63–69.

24.

Wu ,

Duan and

Fu , Complex projective synchronization in coupled chaotic complex dynamical frameworks, Nonlinear Dyn69 (2012), 771–779.

25.

G.M.

Mahmoud and

E.E.

Mahmoud , Complex modified projective synchronization of two chaotic complex nonlinear frameworks, Nonlinear Dyn73 (2013), 2231–2240.

26.

E.E.

Mahmoud and

F.S.

Abood , A new nonlinear chaotic complex model and it's complex antilag synchronization, Complexity2017, ID 3848953.

27.

G.M.

Mahmoud ,

Bountis and

E.E.

Mahmoud , Active control and global synchronization of the complex Chen and Lü frame works, Int J Bifurcat Chaos17 (2007), 4295–4308.

28.

E.E

Mahmoud , Dynamics and synchronization of new hyper-chaotic complex Lorenz framework, Mathematical and Computer Modelling55 (2012), 1951–1962.

29.

E.E

Mahmoud , Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear frame-works with uncertain parameters, J Franklin Inst349 (2012), 1247–1266.

30.

E.E.

Mahmoud , Generation and suppression of a new hyperchaotic nonlinear model with complex variables, Applied Mathematical Modelling38 (2014), 4445–4459.

31.

E.E.

Mahmoud , A novel sort of complex synchronizations, Acta Physica Polonica B48 (2017), 1441–1454.

32.

E.E.

Mahmoud and

S.M.

Abo-Dahab , Dynamical properties and complex anti synchronization with applications to secure communications complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model, Chaos, Solitons and Fractals106 (2018), 273–284.

33.

Wua ,

Wanga and

Lu , Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication, Nonlinear Analysis: Real World Applications13 (2012), 1441–1450.

34.

E.E.

Mahmoud and

F.S.

Abood , A novel sort of adaptive complex synchronizations of two indistinguishable chaotic complex nonlinear models with uncertain parameters and its applications in secure communications, Results in Physics7 (2017), 4174–4182.