Narrow Results

Daisyworld is a reduced-order ecological model that establishes biological homeostasis of the global biota and environment. This work proposes a novel adaptive Daisyworld by considering the classical environment–life interactions, incorporating devastation, greenhouse gas effects and mutations. Climate variability is described by means of the external stimuli that represent Sun’s luminosity. Different mutation mechanisms are investigated considering the temperature-induced changes that define the gray daisies. Either deterministic or random aspects are of concern while incorporating chance on the biota interactions. Numerical simulations are performed using a nonlinear dynamics perspective. Distinct scenarios are of concern while evaluating the different mutation mechanisms and conditions. Complex dynamics are investigated showing the chance and chaos related to the Daisyworld behavior.

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems can generate random dynamics. For instance, the chaotic Chua's circuit coupled to a circuit with a noninvertible I–V characteristic can generate unpredictable dynamics. In general, a nonperiodic time-series with truncated exponential behavior can be converted into unpredictable dynamics using noninvertible transformations. Using a new theoretical framework for chaos and randomness, we investigate some classes of coupled map lattices. We show that, in some cases, these systems can produce completely unpredictable dynamics. In a similar fashion, we explain why some well-known spatiotemporal systems have been found to produce very complex dynamics in numerical simulations. We discuss real physical systems that can generate random dynamics.

In systems theory and science, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems [Aziz-Alaoui & Bertelle, 2009]. In this paper, we use the emergent property of the ultra weak multidimensional coupling of p 1-dimensional dynamical chaotic systems which leads from chaos to randomness.

Generation of random or pseudorandom numbers, nowadays, is a key feature of industrial mathematics. Pseudorandom or chaotic numbers are used in many areas of contemporary technology such as modern communication systems and engineering applications. More and more European or US patents using discrete mappings for this purpose are obtained by researchers of discrete dynamical systems [Petersen & Sorensen, 2007; Ruggiero et al., 2006]. Efficient Chaotic Pseudo Random Number Generators (CPRNG) have been recently introduced. They use the ultra weak multidimensional coupling of p 1-dimensional dynamical systems which preserve the chaotic properties of the continuous models in numerical experiments. Together with chaotic sampling and mixing processes, ultra weak coupling leads to families of (CPRNG) which are noteworthy [Hénaff et al., 2009a, 2009b, 2009c, 2010].

In this paper we improve again these families using a double threshold chaotic sampling instead of a single one.

We analyze numerically the properties of these new families and underline their very high qualities and usefulness as CPRNG when very long series are computed. Moreover, a determining property of such improved CPRNG is the high number of parameters used and the high sensitivity to the parameters value which allows choosing it as cipher-keys. It is why we call these families multiparameter chaotic pseudo-random number generators (M-p CPRNG).

Vibration-based energy harvesting is of increasing importance and there is a current challenge to improve energy harvesting capacity exploiting nonlinear and random effects. This article investigates random effects in a nonlinear energy harvesting system. The system is represented by a magnetoelastic structure with two piezoceramic layers attached to the root of a cantilever beam, obtaining a bimorph generator. The energy harvesting system is subjected to three excitation conditions: pure harmonic, pure random and a combination of harmonic and random excitations. Noise-to-Signal Ratio (NSR) is employed to quantify different combinations of the forcing terms, establishing a procedure to evaluate the system performance. This approach is based on Power Spectral Density (PSD) of input and output signals. Numerical simulations are carried out, identifying the better combinations of harmonic and random excitations for energy harvesting purposes. Discussions about the influence of the kind of response are carried out evaluating the differences between periodic and chaotic motions. Conclusions show that both random and nonlinear effects can be tuned in order to enhance energy harvesting capacity.

Thanks to the simplicity and robustness of its calculation methods, algorithmic (or Kolmogorov) complexity appears as a useful tool to reveal chaotic dynamics when experimental time series are too short and noisy to apply Takens’ reconstruction theorem. We measure the complexity in chaotic regimes, with and without extreme events (sometimes called optical rogue waves), of three different all-solid-state lasers: Kerr lens mode locking femtosecond Ti:Sapphire (“fast” saturable absorber), Nd:YVO₄$+$ Cr:YAG (“slow” saturable absorber) and Nd:YVO₄ with modulated losses. We discuss how complexity characterizes the dynamics in an understandable way in all cases, and how it provides a correction factor of predictability given by Lyapunov exponents. This approach may be especially convenient to implement schemes of chaos control in real time.