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Esculapio Pub. Co., Bologna

This paper offers an overview of morphogenetic processes going on in metal electrodeposition processes and provides a systematisation of the morphology classes identified experimentally in terms of an electrokinetic theory accounting for charge-transfer and masstransport rates. In addition, it provides a review of the modelling work by the authors, based on a reaction-diffusion system coupling morphology with surface chemistry of the growing metal and briefly describes the experimental validation of the model.

We analyze the effects of cross-diffusion on pattern formation in a PDE reaction-diffusion system introduced in Bozzini et al. 2013 to describe metal growth in an electrodeposition process. For this morphochemical model - which refers to the physico-chemical problem of coupling of growth morphology and surface chemistry - we have found that negative cross-diffusion in the morphological elements as well as positive cross-diffusion in the surface chemistry produce larger Turing parameter spaces and favor a tendency to stripeness that is not found in the case without cross-diffusion. The impact of cross-diffusion on pattern selection has been also discussed by the means of a stripeness index. Our theoretical findings are validated by an extensive gallery of numerical simulations that allow to better clarify the role of cross-diffusion both on Turing parameter spaces and on pattern selection. Experimental evidence of cross-diffusion in electrodeposition as well as a physico-chemical discussion of the expected impact of cross diffusion-controlled pattern formation in alloy electrodeposition processes complete the study.

The present paper deals with the pattern formation properties of a specific morpho- electrochemical reaction-diffusion model on a sphere. The physico-chemical background to this study is the morphological control of material electrodeposited onto spherical parti- cles. The particular experimental case of interest refers to the optimization of novel metal- air flow batteries and addresses the electrodeposition of zinc onto inert spherical supports. Morphological control in this step of the high-energy battery operation is crucial to the energetic efficiency of the recharge process and to the durability of the whole energy- storage device. To rationalise this technological challenge within a mathematical modeling perspective, we consider the reaction-diffusion system for metal electrodeposition intro- duced in [Bozzini et al., J. Solid State Electr.17, 467–479 (2013)] and extend its study to spherical domains. Conditions are derived for the occurrence of the Turing instability phe- nomenon and the steady patterns emerging at the onset of Turing instability are investi- gated. The reaction-diffusion system on spherical domains is solved numerically by means of the Lumped Surface Finite Element Method (LSFEM) in space combined with the IMEX Euler method in time. The effect on pattern formation of variations in the domain size is investigated both qualitatively, by means of systematic numerical simulations, and quan- titatively by introducing suitable indicators that allow to assign each pattern to a given morphological class. An experimental validation of the obtained results is finally presented for the case of zinc electrodeposition from alkaline zincate solutions onto copper spheres.

A considerable amount of electrochemical and structural information is available on Au electrodeposition, but its dynamic aspects are still largely ignored. In this paper, an investigation of the microscopic Au electrodeposition dynamics is presented. Extensive sets of SERS spectra during prolonged potentiostatic electrodeposition (∼3 h) are recorded. Two different spot sizes have been used, in order to also obtain some information on the coupling of temporal and spatial fluctuations at the cathodic surface. The time evolution of the SERS background and the intensity of the stretching band of adsorbed CN− have been used as markers of surface morphology and chemistry respectively. Statistical analyses of these quantities allowed extraction of detailed information at the coupled dynamics of SERS enhancement and surface concentration of CN−. The spectroelectrochemical investigation is complemented by SEM observations and mathematical modelling of the coupled dynamics of cathode morphology and CN− sur...

We study the properties of a n2-dimensional Lotka–Volterra system describing competition among n different species with adaptive skills, i.e. whose interaction coefficients are time averages of the species level of interaction over their past. Starting by the case of adaptive competition among species all having the same carrying capacities, we focus our attention on the model obtained on perturbing the carrying capacity of a fixed species, which is made more or less disadvantaged. We prove the existence of a certain class of invariant subspaces and introduce a seven-dimensional reduced model, where n appears as a parameter, which gives full account of existence and stability of equilibria in the system. The relevance of this reduced model to the complete one has also been found when the time dependent regimes have been investigated. Ecologically relevant questions, i.e. species survival and the time dependent behavior of the system have also been analyzed focusing on the role of behavioral adaptation. In particular, we have found that competitive exclusion cannot occur but coexistence is possible in various forms (i.e. competitive stable equilibria and different periodic oscillations).

The period-doubling route to chaos has occupied a prominent position and it is still object of great interest among the different complex phenomena observed in nonlinear dynamical systems. The reason of such interest is that such route to chaos has been observed in many physical, chemical and ecological models when they change over from simple periodic to complex aperiodic motion. In interlinked social–ecological systems (SESs) there might be an apparent great ability to cope with change and adapt if analysed only in their social dimension. However, such an adaptation may be at the expense of changes in the capacity of ecosystems to sustain the adaptation and it could affect the quality of ecosystem goods and services since it could degrade natural renewable and non-renewable resources and generate traps and breakpoints in the whole SES eventually leading to chaotic behaviour. This paper is rooted in previous results on modelling tourism-based SESs, only recently object of theoretical investigations, focusing on the dynamics of the coexistence between mass-tourists and eco-tourists. Here we describe a finer scale analysis of time-dependent regimes in the ranges of the degradation coefficient (bifurcation parameter), for which the system can exhibit coexistence. This bifurcation parameter is determined by objective changes in the real world in the quality of ecosystem goods and services together with whether and how such changes are perceived by different tourist typologies. Varying the bifurcation parameter, the dynamical system may in fact evolve toward an aperiodical dynamical state in many ways, showing that there could be different scenarios for the transition to chaos. This paper provides a further evidence for the period-doubling route to chaos with reference to tourism-based socio-ecological models, and for a period locking behaviour, where a small variation in the bifurcation parameter can lead to alternating regular and chaotic dynamics. Moreover, for many models undergoing chaos via period-doubling, it has been showed that structural perturbations with real ecological justification, may break and reverse the expected period-doublings, hence inhibiting chaos. This feature may be of a certain relevance also in the context of adaptive management of tourism-based SESs: these period-doubling reversals might in fact be used to control chaos, since they potentially act in way to suppress possibly dangerous fluctuations.

In this paper, we consider a general bilinear three dimensional ODE system, whose structure generalizes many mathematical models of biological interest, including many from epidemics. Our main goal is to find sufficient conditions, expressed in terms of the parameters of the system, ensuring that the geometric approach to global stability analysis, due to [M.Y. Li, J.S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal. 27 (4) (1996) 1070–1083], may be successfully applied. We completely determine the dynamics of the general system, including thresholds and global stability of the nontrivial equilibrium. The obtained result is applied to several epidemic models. We further show how the role of new parameters on stability of well-established models may be emphasized.

The analysis of socio-ecological systems requires new, qualitatively distinct, evaluation schemes and appropriate investigation tools that enable an integrated assessment of ecological, social, and economic factors since human land use is a major force driving landscape change, landscape dynamics can be better understood in the context of complex social-ecological systems (SESs). Tourist resorts are deemed as socio-ecological systems, and tourism is a tool for development but could affect the quality of ecosystem goods and services since it could degrade natural renewable and non-renewable resources. In this paper we develop a minimal descriptive model of socio-ecological systems based on tourism, starting from the work of Casagrandi and Rinaldi [Casagrandi, R., Rinaldi, S., 2002. A theoretical approach to tourism sustainability. Conserv. Ecol. 6 (1), 13 (Online). URL: http://www.consecol.org/vol6/iss1/art33], and based on data from a real tourist destination in southern Italy. We develop the model focusing on the interplay among tourists (T), quality of ecosystem goods and services (E), and capital (C), intended as accommodation and entertainment facilities, to make the model more realistic, and to provide a tool for scenario building to support more effectively sustainable management of tourist destination. In particular, we focus on the interplay between tourism and ecosystem quality, distinguishing two main tourist typologies – mass and eco-tourists – and taking into account ecosystem quality in terms of ecosystem goods and services, with a time dependent function, and defining a degradation coefficient of tourist site to be used as a bifurcation parameter. We explore different scenarios, with regards to coexistence of tourist classes and equilibria stability, as generated by variation of the bifurcation parameter. Finally, we discuss the overall results in terms of basins of attraction and stability landscape, and system resilience together with their implications for sustainable tourist destination management.

In the present paper we shall focus on the coupling between surface morphology and surface composition, as a means of understanding the formation of morphological patterns found in electrodeposition (ECD) and, prospectively, as a control strategy of ECD morphology based on manipulations of the surface chemistry (in terms of additive adsorption at the growing cathode). The relevant mathematical background is that of reaction‐diffusion systems: the discussion will be restricted to the case of a single reaction‐diffusion equation for one chemical species adsorbed at the surface of the growing cathode and source terms for both the “chemical” and the “morphological” equations of a simple form. We investigate on the dynamics and we show the arising of spatial patterns induced by diffusion which qualitatively match results found in the experiments.

Lotka-Volterra systems have played a fundamental role for mathematical modelling in many branches of theoretical biology and proved to describe, at least qualitatively, the essential features of many phenomena, see for example Murray [Murray 2002]. Furthermore models of that kind have been considered successfully also in quite different and less mathematically formalized context: Goodwin’ s model of economic growth cycles [Goodwin 1967] and urban dynamics [Dendrinos 1992] are only two of a number of examples. Such systems can certainly be defined as complex ones and in fact the aim of modelling was essentially to clarify mechanims rather than to provide actual precise simulations and predictions. With regards to complex systems, we recall that one of their main feature, no matter of the specific definition one has in mind, is adaptation, i. e. the ability to adjust.

World Scientific, Singapore

We study the properties of a n 2 -dimensional Lotka–Volterra system describing competing species that include behaviorally adaptive abilities. We indicate as behavioral adaptation a mechanism, based on a kind of learning, which is not viewed in the evolutionary sense but is intended to occur over shorter time scales. We consider a competitive adaptive n species Lotka–Volterra system, n ⩾ 3, in which one species is made ecologically differentiated with respect to the others by carrying capacity and intrinsic growth rate. The symmetry properties of the system and the existence of a certain class of invariant subspaces allow the introduction of a 7-dimensional reduced model, where n appears as a parameter, which gives full account of existence and stability of equilibria in the complete system. The reduced model is effective also in describing the time-dependent regimes for a large range of parameter values. The case in which one species has a strong ecological advantage (i.e. with a carrying capacity higher than the others), but with a varying growth rate, has been analyzed in detail, and time-dependent behaviors have been investigated in the case of adaptive competition among four species. Relevant questions, as species survival/exclusion, are addressed focusing on the role of adaptation. Interesting forms of species coexistence are found (i.e. competitive stable equilibria, periodic oscillations, strange attractors).

We deal with the global stability for a well-known population-toxicant model. We make use of a geometrical approach to the global stability analysis for ordinary differential equation which is based on the use of a higher-order generalization of the Bendixson's criterion. We obtain sufficient conditions for the global stability of the unique nontrivial equilibrium. These conditions are expressed in terms of a generic functional describing the population dynamics. In the special case of a logistic-like population dynamics, we get conditions which improve the ones previously known, obtained by means of the Lyapunov direct method.