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Plant-soil negative feedback (PSNF) is the rise in soil of negative conditions for plant performance induced by the plants themselves, limiting the full potential yield and thus representing a loss for the agricultural industry. It has been recently shown that detrimental effects the PSNF has on the growth of plant's biomass can be mitigated by periodically intervening on the plant/soil system, for example by washing the soil. The periodic control inputs were computed by using an average model of the system and then applied in open-loop. In this paper we present two feedback control strategies, namely a PI and a MPC-based controllers, that, by adapting online the duty-cycle of the periodic control input, guarantee precise regulation of the biomass yield and at the same time robustness to unavoidable modeling errors and perturbations acting on the system. The performance of the proposed control strategies is then validated by means of extensive numerical simulations., Comment: Accepted to ECC 2024

We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary differential equation (ODE) describing the dependence of the toxicity on the biomass. We perform a linear stability analysis in the one-dimensional finite space, we derive analytically the conditions for the appearance of Turing instability that gives rise to spatio-temporal patterns emanating from the homogeneous solution, and provide its dependence with respect to the size of the domain. Furthermore, we perform a numerical bifurcation analysis in order to study the pattern formation of the inhomogeneous solution, with respect to the precipitation rate, thus analyzing the stability and symmetry properties of the emanating patterns. Based on the numerical bifurcation analysis, we have found new patterns, which form due to the onset of secondary bifurcations from the primary Turing instability, thus giving rise to a multistability of asymmetric solutions.

Scattering through natural porous formations (by far the most ubiquitous example of disordered media) represents a formidable tool to identify effective flow and transport properties. In particular, we are interested here in the scattering of a passive scalar as determined by a steady velocity field which is generated by a line of singularity. The velocity undergoes to erratic spatial variations, and concurrently the evolution of the scattering is conveniently described within a stochastic framework that regards the conductivity of the hosting medium as a stationary, Gaussian, random field. Unlike the similar one for uniform (in the mean) flow-fields, the problem at stake results much more complex. Central for the present study is the fluctuation of the driving field, that is computed in closed (analytical) form as large time limit of the same quantity in the unsteady state flow regime. The structure of the second-order moment X_{rr}, quantifying the scattering along the radial direction, is explained by the rapid change of the distance along which the velocities of two fluid particles become uncorrelated. Moreover, two approximate, analytical expressions are shown to be quite accurate into reproducing the full simulations of X_{rr}. Finally, the same problem is encountered in other fields, belonging both to the classical and to the quantum physics. As such, our results lend themselves to be used within a context much wider than that exploited in the present study., Comment: 21 pages, 5 figures

Plant-soil feedback is recognized as a causal mechanism for the emergence of vegetation patterns of the same species especially when water is not a limiting resource (e.g. humid environments). Nevertheless, in the field, plants rarely grow in monoculture but compete with other plant species. In these cases, plant-soil feedback was shown to play a key role in plant-species coexistence. Using a mathematical model consisting of four PDEs, we investigate mechanisms of inter- and intra-specific plant-soil feedback on the coexistence of two competing plant species. In particular, the model takes into account both negative and positive feedback influencing the growth of the same and the other plant species. Both the coexistence of the plant species and the dominance of a particular plant species is examined with respect to all model parameters together with the emergence of spatial vegetation patterns.

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of forest/grassland value. The system displays multiple steady states corresponding to different forest densities as well as regimes characterized by both stable and unstable limit cycles. We derive analytically the conditions with respect to the model parameters that give rise to various types of codimension-one criticalities such as transcritical, saddle-node, and Andronov-Hopf bifurcations and codimension-two criticalities such as cusp and Bogdanov-Takens bifurcations. We also perform a numerical continuation of the branches of limit cycles. By doing so, we reveal turning points of limit cycles marking the appearance/disappearance of sustained oscillations. These far-from-equilibrium criticalities that cannot be detected analytically give rise to the abrupt loss of the sustained oscillations, thus leading to another mechanism of catastrophic shifts

Disciplinary diversity is being recognized today as the key to establish a vibrant academic environment with bigger potential for breakthroughs in research and technology. However, the interaction of several factors including policies, and behavioral attitudes put significant barriers on advancing interdisciplinarity. A "cognitive rigidity" may rise due to reactive academic lobbying favouring inbreeding. Here, we address, analyse and discuss a mathematical model of lobbying and interdisciplinarity dynamics in Academia. The model consists of four coupled non-linear Ordinary Differential Equations simulating the interaction between three types of academic individuals and a state reflecting the rate of knowledge advancement which is related to the level of disciplinary diversity. Our model predicts a rich nonlinear behaviour including multiplicity of states and sustained periodic oscillations resembling the everlasting struggle between the "new" and the "old". The effect of a control policy that inhibits lobbying is also studied. By appropriate adjustment of the model parameters we approximated the jump/phase transitions in breakthroughs in mathematical and molecular biological sciences resulted by the increased flow of Russian scientists in the USA after the dissolution of the Soviet Union starting in 1989, the launch of the Human Genome Project in 1992 and the Internet diffusion starting in 2000.