arXiv subjects

Gaetana Gambino

Publications and source records attributed to Gaetana Gambino.

4 recordsLinked to original sources

arXiv2026

On a phenotype-structured Shigesada--Kawasaki--Teramoto model: Turing instability and pattern selection under fast phenotype switching

The Shigesada-Kawasaki-Teramoto (SKT) model has become a classical modelling framework for studying spatial segregation and cross-diffusion-driven pattern formation in competing populations. This model assumes phenotypic homogeneity, but phenotypic variability persists within any population and can strongly influence both ecological and evolutionary dynamics. In this paper, we present a generalised phenotype-structured formulation of the SKT model that accounts for phenotypic variability. In this formulation, the competing populations are continuously structured across some phenotype state spaces. Population members move and compete in phenotype-dependent ways, and can also switch between different phenotype states. First we show how a form of the classical SKT model, wherein parameters are written in terms of continuous weighted averages of the phenotype-dependent functions of the generalised structured model, with weights given by the phenotype distributions of the two populations, can be obtained in the quasi-invariant regime of fast phenotype switching. Then, still assuming fast phenotype switching and extending classical Turing-like linear and weakly nonlinear analyses, we explore the conditions for the emergence of spatial patterns, identify a Turing-type bifurcation threshold leading to pattern formation, and investigate the nature of such a bifurcation (super- or sub-critical) as well as the stability of the patterned state. The results obtained make it possible to draw connections between phenotype-dependent model functions and the emergence of population-scale aggregate spatial dynamics, showing in particular how phenotype distributions can act as effective control parameters for Turing instability and pattern selection. These findings are complemented by numerical simulations, which validate the formal asymptotics and confirm the predictions of the pattern formation analyses.

q-bio.PE↗

arXiv2026

A Damage-Driven Model for Duchenne Muscular Dystrophy: Early-Stage Dynamics and Invasion Thresholds

We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis system describing the interaction between healthy tissue, damaged fibers, immune cells and inflammatory signals. We establish the global well-posedness of the system and investigate the early-stage dynamics through linearization around the healthy equilibrium. Our analysis shows that diffusion does not induce Turing instabilities, so that spatial heterogeneity cannot arise from diffusion-driven mechanisms. Instead, disease progression occurs through invasion processes. We derive explicit conditions for the onset of invasion, interpreted as an effective damage reproduction threshold and characterize the minimal propagation speed of pathological fronts, showing that the dynamics is governed by a pulled-front mechanism. Numerical simulations support the analytical results and confirm the transition between decay and invasion. These results provide a mathematical framework for early-stage disease progression and indicate that spatial spreading arise from the expansion of localized damage rather than from intrinsic pattern-forming mechanisms.

math-ph↗

arXiv2026

Nonclassical Turing instabilities induced by superdiffusive transport in FitzHugh-Nagumo dynamics

We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A linear stability analysis yields explicit expressions for the instability threshold and the critical wavenumber and shows that superdiffusion modifies the band of unstable modes and the characteristic spatial scale of emerging patterns. We show that the threshold depends only on the ratio of the fractional exponents and on the kinetic parameters, while the spatial scale is controlled by the diffusion orders and the domain size. When the diffusion orders differ, spatial instabilities may occur even in regimes where the activator diffuses faster than the inhibitor, due to the combined effect of diffusion rates, anomalous scaling and system size. This leads to instability mechanisms that depart from the classical activator-inhibitor framework. A weakly nonlinear analysis near threshold provides the amplitude equation governing nonlinear saturation and reveals that superdiffusion promotes subcritical behavior. We also analyze the interaction between stationary and oscillatory instabilities near Turing-Hopf codimension-two points. All analytical results are supported by numerical simulations.

nlin.PS↗

arXiv2012

Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System

In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control.

nlin.CD↗