Maxima of mean transient time versus driving amplitude were found for weakly dissipated Duffing oscillator. In the neighborhood of peak of mean transient time an approximate power-law dependence was found. This behavior was compared with scaling in the vicinity of crisis point and interpreted as crossing of two neighboring crisis points which appears with decrease of driving amplitude. At this ...

In the present effort, a data-driven modeling approach is undertaken to forecast aperiodic responses of non-autonomous systems. As representative system, harmonically forced Duffing oscillator considered. Along with it, an experimental prototype studied. Data corresponding chaotic motions are obtained through simulations oscillators hardening and softening characteristics experiments bistable o...

In this paper, an improved technique for constructing Chaotic Shift Keying (CSK) for transmitting digital signals is introduced. In contrast to the classical methods where only two chaotic attractors, representing logic 0 and logic 1 are used to build CSK, the proposed system allows the chaotic transmitted signal to alternate among four different chaotic attractors. In addition, the transmitter...

Chaotic systems exhibit highly nonlinear, complex and unpredictable behaviors. Thereby, these systems have received much attention in a variety of fields over the past few decades. In this paper we develop a particle filter algorithm to solve the problem of chaotic state and unknown input estimation from arbitrarily nonlinear time series. Thus, even if there exist Gaussian or non-Gaussian noise...

Weak signal detection is very important in the downhole acoustic telemetry system. This paper introduces the Duffing oscillator weak signal detection method for the downhole acoustic telemetry systems. First, by solving the Duffing equation, analyzed the dynamics characteristic of Duffing oscillator and weak signal detection principle; and then on this basis, built Duffing oscillator circuit ba...

With the significant development in communication systems especially in the public channels through which our information travels, there are more increasing in the channels problems. The information security is the important one that should be enhanced. This paper presents a chaos-based speech scrambling system. Chaotic maps have been successfully used for large-scale data encryption such as im...

In this paper, we investigate the chaotic behavior of ordinary differential equations with a homoclinic orbit to a dissipative saddle point under an unbounded random forcing driven by a Brownian motion. We prove that, for almost all sample pathes of the Brownian motion in the classical Wiener space, the forced equation admits a topological horseshoe of infinitely many branches. This result is t...

We show how a topological model which describes the stretching and squeezing mechanisms responsible for creating chaotic behavior can be extracted from the neural spike train data. The mechanism we have identified is the same one ("gateau roule," or jelly-roll) which has previously been identified in the Duffing oscillator [Gilmore and McCallum, Phys. Rev. E 51, 935 (1995)] and in a YAG laser [...

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the expansion coefficients. Here we study the structure and dynamics of these differential equations when the original system has Hamiltonian structure, has multiple t...