Related papers: Correlated noise in a logistic growth model
We study the steady state properties of an insect (spruce budworm) outbreak model in the presence of Gaussian white noise. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution function…
We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…
In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…
Instead of a continuous system driven by Gaussian white noise, logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise, which shows a phenomenon different from…
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
We discuss a model of a system of interacting populations for the case when: (i) the growth rates and the coefficients of interaction among the populations depend on the populations densities: and (ii) the environment influences the growth…
We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance,…
Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…
It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from…
Many natural and social phenomena are characterized by synchronization. The Kuramoto model, taking into account the basic ingredients for observing synchronized states, allows to study mathematically synchronization in a simplified but…
Accurately predicting drug responses to cancer is an important problem hindering oncologists' efforts to find the most effective drugs to treat cancer, which is a core goal in precision medicine. The scientific community has focused on…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
Metastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive…
We study the effect of a weak random additive noise in a linear chain of N locally-coupled logistic maps at the edge of chaos. Maps tend to synchronize for a strong enough coupling, but if a weak noise is added, very intermittent…
We study the combined impact of a colored environmental noise and demographic noise on the extinction risk of a long-lived and well-mixed isolated stochastic population which exhibits the Allee effect. The environmental noise modulates the…
We investigate the behavior of dissipative particle dynamics (DPD) with time-correlated random noise. A new stochastic force for DPD is proposed which consists of a random force whose noise has an algebraic correlation proportional to 1/t…
When a collection of phenotypically diverse organisms compete with each other for limited resources, with competition being strongest amongst the most similar, the population can evolve into tightly localised clusters. This process can be…
In a recent study the initial rise of the mutual information between the firing rates of N neurons and a set of p discrete stimuli has been analytically evaluated, under the assumption that neurons fire independently of one another to each…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…