Related papers: Pattern formation and nonlocal logistic growth

In the well known logistic map, the parameter of interest is weighted by a coefficient that decreases linearly when this parameter increases. Since such a linear decrease forms a specific case, we consider the more general case where this…

We consider a parameter dependent periodic-logistic problem with a logistic term involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary…

We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a…

Logistic growth of diffusing reactants on spatial domains with long range competition is studied. The bifurcations cascade involved in the transition from the homogenous state to a spatially modulated stable solution is presented, and a…

The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…

This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…

Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…

It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…

In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…

Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…

For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…

Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…

A time series of fractal dimension values of urban form can form a fractal dimension curve and reflects urban growth. In many cases, the fractal dimension curves of cities can be modeled with logistic function, which in turn can be used to…

Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…

We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a…