相关论文: Planktons discrete-time dynamical systems

The dynamics of a packages diffusion process within a selforganized network is analytically studied by means of an extended $f$% -spin facilitated kinetic Ising model (Fredrickson-Andersen model) using a Fock-space representation for the…

Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

Planktonic active matter represents an emergent system spanning different scales: individual, population and community; and complexity arising from sub-cellular and cellular to collective and ecosystem scale dynamics. This cross-scale…

Microorganisms self-organize in very large communities exhibiting complex fluctuations. Despite recent advances, still the mechanism by which these systems are able to exhibit large variability at the one hand and dynamical robustness on…

Two novel extended semi-discrete KP-type systems, namely partial differential-difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the…

Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…

Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the…

We first consider the Hamiltonian formulation of $n=3$ systems in general and show that all dynamical systems in ${\mathbb R}^3$ are bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. We…

A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

We study the evolution of a system of $N$ interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems.…

For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…