Road traffic volumes in intercity roads are generally estimated by probability functions, statistical techniques or meta-heuristic approaches such as artificial neural networks. As the road traffic volumes depend on input variables and mainly road geometrical design, weather conditions, day or night time, weekend or national holidays and so on, these are also estimated by pattern recognition te...

In order to achieve chaotic signal processing, a dedicated chaos processor is required. The chaos processor is composed of two parts: chaos signal generation and chaos signal retrieval (Fig. 1). Chaos signal generation is used to generate chaos signal, while chaos signal retrieval is used to retrieve initial state of received chaos signal. Since chaos signal is analog in nature, with convention...

Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...

Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 14, which is Bernoulli στ -shift rule and is a member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of rule 14, whether it possesses chaotic attractors or not. In t...

We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math. Biol. 74 (2012) 2383-2402] in the study of a population in which reproduction occurs at a discrete instant of time whereas death and competition take place continuously during the season. We show analytically that there exists a ...

We study the existence of snap-back repellers, hence the existence of transversal homoclinic orbits in a discrete-time neural network. Chaotic behaviors for the network system in the sense of Li and Yorke or Marotto can then be concluded. The result is established by analyzing the structures of the system and allocating suitable parameters in constructing the fixed points and their pre-images f...

We test a Markov chain approximation to the segment description (Li, 2007) of chaos (and turbulence) on a tent map, the Minea system, the Hénon map, and the Lorenz system. For the tent map, we compute the probability transition matrix of the Markov chain on the segments for segment time length (iterations) T = 1, 2, 3, 100. The matrix has 1, 2, 4 tents corresponding to T = 1, 2, 3; and is almos...

We demonstrate that many physical systems possess an often overlooked property known as a partial-ordering structure. The detection and analysis of this special geometric property can be crucial for understanding a system's dynamical behavior. We review here the fundamental dynamical features common to all such systems, and describe how the partial ordering imposes interesting restrictions on t...

This paper investigates the adaptive control and synchronization of an uncertain modified hyperchaotic Lü system recently discovered by Wang, Zhang, Zheng and Li (2006). This paper deploys nonlinear control for controlling the hyperchaos of the modified hyperchaotic Lü system with unknown parameters and then synchronizing two identical modified hyperchaotic Lü systems with unknown parameters. F...

In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve   f x of the difference equation,   1 n n X f X   , are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos...