Fighting Risky Population Synchronization: Desynchronization and Stabilization in Spatially Structured Ecological Systems

Population synchronization exists ubiquitously in ecological systems, of which the underlying causes and the roles in species extinction remain a perplexing puzzle. It is generally believed that the coherence of population dynamics is detrimental and regarded as a major cause of global extinction. A central but unsolved question in ecology of great importance for conservation and biological control is how to destroy the pernicious coherent structures. Here, a top-down approach is adopted to tackle the challenge. A feedback strategy accordingly is applied to stabilize the metacommunity, i.e., to reduce excessive metapopulation fluctuations by means of introducing or removing a planned number of individuals. As a result, the feedback desynchronizes correlated population oscillations, giving rise to either complex asynchronous traveling waves or "amplitude death"; cessation of all individual population cycles. Together with the construction of corridors, my method may provide an efficient way to protect those species threatened as a result of, e.g. habitat fragmentation. I anticipate my essay provides a general mechanism against widespread harmful synchronization in physical and biological systems, for example, for developing a "brain anti-pacemaker" for neurological diseases such as Parkinson's disease and epilepsy closely linked to pathologically synchronized neuronal discharges

Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials

In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are established