The problem of creating chaos for a class of nonlinear systems with backlash function is studied in this paper. By utilizing the characteristic of backlash function, some criteria for guaranteing the nonlinear system to be horseshoe type of chaos are derived based on S̆i’lnikov heterclinic theorem and S̆i’lnikov homoclinic theorem. Examples and simulations are given to illustrate the effectivenes...

We present experimental results on stabilizing unstable periodic orbits of an autonomous chaos oscillator based on a simple electronic circuit. Control is achieved by applying the difference between the actual and a delayed output signal of the oscillator. The quality of chaos control can be measured via the strength of perturbation. The dependence on the delay time shows a characteristic reson...

different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. evolutionary phenomena are discussed through bifurcation analysis leading to chaos. some tools of nonlinear dynamics, such as lyapunov characteristic exponents (lce), lyapunov numbers, correlation dimension, etc. are calculated ...

‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

Based on an information theory approach we suggest a quantitative characteristic for evaluating the degree of chaotic synchronization. The proposed characteristic is tested for the cases of complete and phase synchronization of chaos. It is shown that this characteristic is stable with respect to the influence of small noise and nonlinear signal distortion.

This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzymesubstrate interactions in the nutrient and respiratory chains, which leads to the self-organization in autocatalysis of the integral metabolic process in cells. The auto-oscillations organize themselves in the to...

Controlling chaos is a topic in nonlinear dynamics which attracted a great deal of work in the last twenty years. Even though there are more definitions of the chaos [4], a distinctive characteristic of the chaotic behavior of a dynamical system is its sensitive dependence on the initial conditions. Generally, chaos is believed to be harmful because in many cases it can lead to disasters. Chaot...

We have performed several experiments to study the possible use of chaos in simulated evolution. Chaos is often associated with dynamic situations in which there is feedback, hence there is speculation in the literature that chaos is a factor in natural evolution. We chose the iterated prisoner’s dilemma problem as a test case, since it is a dynamic environment with feedback. To perform an init...

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis’ q-expon...

It is one of the most puzzling problems in astrophysics to understand the anomalous resistivity in collisionless magnetic reconnection that is believed extensively to be responsible for the energy release in various eruptive phenomena. The magnetic null point in the reconnect current sheet, acting as a scattering center, can lead to chaotic motions of particles in the current sheet, which is on...