We analyze endogenous pattern formation resulting from forward-looking optimizing behavior of economic agents in the presence of spatial spillovers modelled by continuous kernels. We use Fourier methods to identify necessary and sufficient conditions for the emergence of optimal agglomeration through an optimal spillover induced instability of a spatially homogeneous steady state. We apply our ...

Abstract-The asymptotic stability regions for the patterned steady-state solution in a two-particle catalytic CSTR, established by Arce and Ramkrishna (1991, A.IC1I.E. J. 37,98-l lo), are constructed using two approaches, Liapunov’s direct method and the construction of a trapping region. In addition, the trapping regions are also constructed for uniform steady-state solutions. Stability region...

Migrating cells measure the external environment through receptorbinding of specific chemicals at their outer cell membrane. In this paper this non-local sampling is incorporated into a chemotactic model. The existence of global bounded solutions of the non-local model is proven for bounded and unbounded domains in any space dimension. According to a recent classification of spikes and plateaus...

We study the long-time effect of noise on pattern formation for the aggregation model. We consider aggregation kernels that generate patterns consisting of two delta-concentrations. Without noise, there is a one-parameter family of admissable equilibria that consists of two concentrations having whose mass is not necessary equal. We show that when small amount of noise is added, the heavier con...

A general reaction–diffusion system modelling glycolysis is investigated. The parameter regions for the stability and instability of the unique constant steady-state solution is derived, and the existence of time-periodic orbits and non-constant steady-state solutions are proved by the bifurcation method and Leray–Schauder degree theory. The effect of various parameters on the existence and non...

Mathematical studies of drug induced geometric visual hallucinations include three components: a model (or class of models) that abstracts the structure of the primary visual cortex V1; a mathematical procedure for finding geometric patterns as solutions to the cortical models; and a method for interpreting these patterns as visual hallucinations. Ermentrout and Cowan used the Wilson–Cowan equa...

We study the interior spike solutions to a steady state problem of the shadow system of the Gierer-Meinhardt system arising from biological pattern formation. We rst show that at a nondegenerate peak point the interior spike solution is locally unique and then we establish the spectrum estimates of the associated linearized operator. We also prove that the corresponding solution to the shadow s...

Analogous to Peierls' arguments for the 'anomalous' Hall in metals I demonstrate that the Hall anomaly in the mixed state of superconductors, the sign change of the Hall resistivity, is a property of a vortex many-body correlation, and show that the anomaly is due to the competition between vortex vacancies and interstitials. Within this vortex many-body effect picture, many features of the com...

We study the incentive to cooperate in a nation comprised of citizens and immigrants. The level of cooperation is governed by a steady state under population dynamics, along with the behavior of individual citizens and immigrants. We provide an equilibrium characterization, exhibiting a uniquely determined positive level of cooperation in society. We then use this framework to study the impact ...

In social networks of human individuals, social relationships do not necessarily last forever as they can either fade gradually with time, resulting in "link aging," or terminate abruptly, causing "link deletion," as even old friendships may cease. In this paper, we study a social network formation model where we introduce several ways by which a link termination takes place. If we adopt the li...