Abstract:Much progress has been made in the research of synchronization for chaotic real or complex nonlinear systems. In this paper we introduce a new type of synchronization which can be studied only for chaotic complex nonlinear systems. This type of synchronization may be called complex lag synchronization (CLS). A definition of CLS is introduced and investigated for two identical chaotic complex nonlinear systems. Based on Lyapunov function a scheme is designed to achieve CLS of chaotic attractors of these systems.

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The objective of this work is to analyze the impact of magneto-hydrodynamics flow across a stretching layer in the existing magnetic sector. The classifying boundary layer equations are converted to a set of non-linear equations by taking advantage of similarity structures. The transformed scheme is mathematically resolved by the homotopy analysis method. Results are measured numerically and plotted graphically for velocity and temperature distribution. Furthermore, flow and heat transfer effects for different physical parameters such as the stretching parameter, mixed convection parameter, magnetic parameter, heat generation coefficient, and Prandtl number are analyzed. Some physical effects reveal that an increase in the Hartmann number raises the fluid’s boundary layer that shows the reverse phenomena of Lorentz force because the speed of the free stream transcends the stretching surface. Upon verifying the homology of the current study with some past investigations, a good harmony is revealed. The velocity of the fluid flow was initially considered to be an increasing function of heat generation, buoyancy parameter, and magnetic field strength, but it later revealed as a decreasing function of the Prandtl number.

The present article uses a modified G ′ G -expansion method and the generalized Kudryashov method on Klein-Fock-Gordon (KFG) equation and receives some stable and functional solutions. The obtained results are checked by putting backwards into the physical model and are very beneficial over various existing processes. The diverse variety of stable and functional outcomes such as kink-type shape, bright and dark lump shape, bright and dark singular kinky shape, periodic bright and dark lump shape, multiple bright and dark lump shape, the lump with rough wave shape, the rough wave shape and the kinky shape are taken. The above procedure could also be employed to get stable and functional solutions for other integral and fractional nonlinear models in physics, mathematics, and engineering.

New hyperchaotic nonlinear model inclusive complex variables have been introduced in this paper. This model has attributes that differentiate it from several of the models contemplated as of late in literature, for example, (i) this model is a high-dimension (9D), (ii) the new model has hyperchaotic conduct with four positive Lyapunov exponents, (iii) the attractors of our model has four scroll. Features and characteristics of this model containing Hamiltonian, invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic (hyperchaotic) accomplishment are studied. On the confirmation of stability theory and active control technique, an approach is made to play out the complete and phase synchronizations of two identical hyperchaotic attractors of our model. The efficiency of the gained outcomes is revealed by a simulation illustration. The phase synchronization outcomes were utilized to build up a straightforward application in secure communication. Numerical effects computed to show the hyperchaotic synchronizations of a hyperchaotic model and to test the control powers scientific expressions gravity.