We show that Bayesian ex post aggregation is unstable with respect to refinements. Suppose a group of Bayesians use ex post aggregation. Since it is a joint problem, each agent’s problem is captured by the same model, but probabilities and utilities may vary. If they analyze the same situation in more detail, their refined analysis should preserve their preferences among acts. However, ex post ...

A complex Ginzburg-Landau type amplitude equation which is valid in the Hopf region of phase space near an instability threshold admits solutions like antisymmet-ric pulses traveling in alternate direction from a core. Such pulse solutions come out as a steady state solution of the system on moving frame. The pulses have spatial profile like Hermite polynomial of order unity with the negative(p...

Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction-diffusion model in which predator mortality is neither a constant nor an unbounded functio...

In this paper I show that Proclus is an adherent of the Classical Model of Science as set out elsewhere in this issue, and that he adjusts certain conditions of the Model to his Neoplatonic epistemology and metaphysics. In order to show this, I develop a case study concerning philosophy of nature, which, despite its unstable subject matter, Proclus considers to be a science. To give this scienc...

We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE...

We present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with selfas well as crossdiffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; Hopf and Turing bifurcation in a spatial domain is p...

In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive the symbolic conditions for Hopf and Turing bifurcation in the spatial domain. Based on the stab...

Great progress has been made in bifurcation control of systems described by ordinary differential equations. However, the Hopf and Turing patterns is seldom reported reaction-diffusion systems, which formed partial In this paper, a hybrid synthesis combining state feedback firstly devised marine planktonic ecosystem. The instability condition criterion are derived through carrying out eigenvalu...