We investigate nonlinear dynamical systems from the mode competition point of view, and propose the necessary conditions for a system to be chaotic. We conjecture that a chaotic system has at least two competitive modes (CM’s). For a general nonlinear dynamical system, we give a simple, dynamically motivated definition of mode suitable for this concept. Since for most chaotic systems it is diff...

We numerically investigate chaotic behavior in autonomous nonlinear models of fractional order. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in ð0; 1 , based on frequency domain arguments, and the resulting equivalent models are studied. Two chaotic models are considered in this study; an electronic chaotic oscillator, ...

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. Unfortunately, despite the advantages of chaotic systems, Such as, noise-like correlation, easy hardware implementation, multitude of chaotic modes, flexible control of their dynamics, chaotic self-synchronization phenomena and potential communication confidence due to the very dynami...

The predictability of a chaotic series is limited to a few future time steps due to its sensitivity to initial conditions and the exponential divergence of the trajectories. Over the years, streamflow has been considered as a stochastic system in many approaches. In this study, the chaotic nature of daily streamflow is investigated using autocorrelation function, Fourier spectrum, correlation d...

technique for enhancing the pseudorandomness of digital chaotic oscillators through a nonlinear XOR-based operation with rotation and feedback. The technique allows full utilization of the chaotic output as pseudorandom number generators and improves throughput without a significant area penalty. Digital design of a third-order chaotic system with maximum function nonlinearity is presented with...

A crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles. The fractal dimension of the resulting chaotic saddle increases through the crisis. We present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of cris...

Based on the fractional order of nonlinear system for love model with a periodic function 10 as an external force, analyzed the characteristics of the chaotic dynamic in this study. The 11 relationship between the chaotic dynamic of the fractional-love model with the external force and 12 the fractional-order system was analyzed when the parameters are fixed. Further, we also studied 13 the rel...

One of the main problems in chaotic time series prediction is that the underlying nonlinear dynamics is usually unknown. Using a nonlinear predictor to predict a chaotic time series usually puts a limit on the accuracy since the nonlinear predictor is basically an approximation of the unknown nonlinear mapping. In this paper, we propose using fusion of predictors as a method to improve the perf...

In this paper, the motion control of a mobile robot, which is based on a specific type of chaotic systems, is studied. These systems produce the well-known from the nonlinear theory double-scroll chaotic attractors. So, the proposed motion control strategy of the mobile robot is based on a chaotic path planning generator in order to cover a terrain fast and with unpredictable way. For choosing ...

This article presents a new modified adaptive function projective synchronization method for the synchronization of time-delayed chaotic systems. The adaptive function projective synchronization controller and identification parameter laws are designed on the basis of Lyapunov-Krasovskii functional approach to stabilize the error system which makes the state vector of two chaotic systems asympt...