Many advancements have been made in the field of topological mechanics. The majority works, however, concerns invariant a linear theory. We, this work, present generic prescription defining indices which accommodates non-linear effects mechanical systems without taking any approximation. Invoking tools differential geometry, Z-valued quantity terms Poincare-Hopf index, that features zero modes ...

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits discrete-time representation in terms discrete gradient, with same energy function but modified damping and interconnection matrices. By construction, proposed sampled-data guarantees match...

Abstract Using nonlinear chaotic systems for secure communication is an application field presented in recent published research. This paper aims at improving the security of signal transmission using encryption. The proposed approach uses a combined analogue and discrete-time structure, both emitter synchronizing receiver. prototype system used similar to Lorenz oscillator. Our study presents ...

The sinc method is known as an ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical mod...

Chaos based communications have drawn increasing attention over the past years. Chaotic signals are derived from non-linear dynamic systems. They are aperiodic, broadband and deterministic signals that appear random in the time domain. Because of these properties, chaotic signals have been proposed to generate spreading sequences for wide-band secure communication recently. Like conventional DS...

‎In this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of Lyapunov‎ ‎method‎. ‎To examine the obtained results‎, ‎we employe the developed techniques on test examples‎.

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

Two phenomena can produce chattering: switching of input control signal and the large amplitude of this switching (switching gain). To remove the switching of input control signal, dynamic sliding mode control (DSMC) is used. In DSMC switching is removed due to the integrator which is placed before the plant. However, in DSMC the augmented system (system plus the integrator) is one dimension bi...

Dynamic sliding mode control (DSMC) of nonlinear systems using neural networks is proposed. In DSMC the chattering is removed due to the integrator which is placed before the input control signal of the plant. However, in DSMC the augmented system is one dimension bigger than the actual system i.e. the states number of augmented system is more than the actual system and then to control of such ...

 Abstract    This paper gives a survey of the theory and practice of nonlinear ABS methods including various types of generalizations and computer testing. We also show three applications to special problems, two of which are new.