Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

The dynamical emergence (and subsequent intermittent breakdown) of collective behavior in complex systems is described as a non-Poisson renewal process, characterized by a waiting-time distribution density $\psi (\tau)$ for the time intervals between successively recorded breakdowns. In the intermittent case $\psi (t)\sim t^{-\mu}$, with complexity index $\mu$. We show that two systems can exchange information through complexity matching and present theoretical and numerical calculations describing a system with complexity index $\mu_{S}$ perturbed by a signal with complexity index $\mu_{P}$. The analysis focuses on the non-ergodic (non-stationary) case $\mu \leq 2$ showing that for $\mu_{S}\geq \mu_{P}$, the system $S$ statistically inherits the correlation function of the perturbation $P$. The condition $\mu_{P}=\mu_{S}$ is a resonant maximum for correlation information exchange.Comment: 4 pages, 1 figur

Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.Comment: 30 page

Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Assessment of Seagrass Floral Community Structure from Two Caribbean Marine Protected Areas

Seagrass communities represent spatially complex and biomass producing systems comprised of intermixed seagrass and algal species. We investigated shallow water communities from two Marine Protected Areas (MPAs) in the Caribbean: St. John, United States Virgin Islands and Cayos Cochinos, Honduras. St. John sites (4) lie within the Virgin Islands National Park and the Coral Reef National Monument and are designated within an UNESCO Biosphere Reserve. Honduran sites (4) lie within the designated Marine National Monument. Our results indicate that both MPAs were dominated by Thalassia testudinum with spatial coverage and shoot density significantly greater in Honduras. Many sites also showed substantial cover of Syringodium filiforme, which was significantly greater in St. John. Most major algal groups showed significant differences between MPAs and among sites within locations. Specifically, Halimeda, Penicillus, Udotea, Galaxaura, and Dictyosphaeria were significantly more abundant in Honduras, while Padina and Avrainvillea were significantly greater from St. John. Additionally, only Honduran sites showed the presence of coral colonies (Montastrea and Porites) within their seagrass beds. Floral community level analyses demonstrated significant differences among almost all site comparisons suggesting relatively distinct floral communities exist within each of these regions, but both MPAs maintain high spatial coverage of seagrasses providing critical ecosystem services

Beyond the Death of Linear Response: 1/f optimal information transport

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.Comment: 4 pages, 2 figures, 1 table, in press on Phys. Rev. Let

Aging and Rejuvenation with Fractional Derivatives

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2<mu <3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord, is given by ord=3-mu . A brand new system is characterized by the degree ord=mu -2. If the system is prepared at time -ta<0$ and the observation begins at time t=0, we derive the following scenario. For times 0<t<<ta the system is satisfactorily described by the fractional derivative with ord=3-mu . Upon time increase the system undergoes a rejuvenation process that in the time limit t>>ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.Comment: 11 pages, 4 figure

Analytical Study on the Influence of Parasitic Elements in a Memristor

We study a memristive circuit with included parasitic elements, such as capacitance and inductance. In the multiple-scale scheme, we analytically show how the parasitic elements affect the voltage and the current. Finally, we provide an analytical expression for the intersection point coordinates, through which we discuss the functional behavior of the pinched hysteresis loop versus the operating frequency and the parasitic elements