In this paper we describe the design of a multiagent system based on simple interaction rules that can generate different overall behaviours, from asymptotically stable to chaotic, verified by the corresponding largest Lyapunov exponent. We show that very small perturbations can have a great impact on the evolution of the system, and we investigate some methods of controlling such perturbations...

A new 4D fractional-order chaotic system, which has an infinite number of equilibrium points, is introduced. There is no-chaotic behavior for its corresponded integer-order system. We obtain that the largest Lyapunov exponent of this 4D fractional-order chaotic system is 0.8939 and yield the chaotic attractor. A chaotic synchronization scheme is presented for this 4D fractional-order chaotic sy...

Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitions to equipartitions, and the scaling beha...

The ultrafast relaxation of small clusters immediately after ionization is studied. For small Hgn clusters we determine the fragmentation-time distributions induced by ionization. A dramatic change of the fragmentation behaviour occurs when the temperature before ionization reaches the melting point of the neutral clusters. The ultrafast dynamics depends nonlinearly on initial conditions regard...

We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of N , N ≥ 2, symbols and with C1 diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic, exhibiting simultaneously ergodic measures with positive, negative, and zero exponents. We derive a multifractal analysis for the topological entropy of the level sets...

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...

In this paper, fractal dimensional analysis is used to investigate the Tamil Nadu rainfall dynamics. Here, the time series data of Tamil Nadu rainfall (annual, south west and northeast) has been analyzed using Detrended fluctuation analysis (DFA). For estimating the 110 years rainfall data, the scaling exponent analysis is used. The result shows a varying degree of persistence over shorter and ...

A cycle expansion for the Lyapunov exponent of a product of random matrices is derived. The formula is non-perturbative and numerically effective, which allows the Lyapunov exponent to be computed to high accuracy. In particular, the free energy and the heat capacity are computed for the one-dimensional Ising model with quenched disorder. The formula is derived by using a Bernoulli dynamical sy...