Cristina M. González, Javier M. Buldú, M. C. Torrent, and Jordi García-Ojalvo Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom 11, E-08222 Terrassa, Spain Nonlinear Dynamics and Chaos Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain Received 30 March 2007; revised manuscript received 11 August 2007; pub...

Recently Hu, Tung, Gao, and Cao [Phys. Rev. E 72, 056207 (2005)] investigated the 0-1 test for chaos. By looking at random data and at data stemming from the one-dimensional logistic map they concluded that the test is unreliable. We explain why their criticism is unfounded.

Recently, a new scheme was proposed for deniable authentication. Its main originality lied on applying a chaos-based encryption-hash parallel algorithm and the semi-group property of the Chebyshev chaotic map. Although original and practicable, its insecurity and inefficiency are shown in this paper, thus rendering it inadequate for adoption in e-commerce.

Since Li and Yorke first gave the definition of chaos by using strict mathematical language in 1975 [1], the research on chaos has greatly influenced modern science, not just natural sciences but also several social sciences, such as economics, sociology, and philosophy. The theory of chaos convinced scientists that a simple definite system can produce complicated features and a complex system ...

We study stochastic elliptic PDEs driven by multiplicative Gaussian white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an e ective tool to study such equations and present the corresponding solvability results.

By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equil...

In two new papers [2] and [8], sharp general quantitative bounds are given to complement the wellknown fourth moment theorem of Nualart and Peccati, by which a sequence in a …xed Wiener chaos converges to a normal law if and only if its fourth cumulant converges to 0. The bounds show that the speed of convergence is precisely of order the maximum of the fourth cumulant and the absolute value of...

Walking, as an important transportation mode, plays a large part in urban transportation systems. This mode is of great importance for planners and decision-makers because of its impact on environmental and health aspects of communities. However, this mode is so complex in nature that makes it difficult to study or model. On the other hand, chaos theory studies complex dynamical nonlinear syste...

Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...