Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem

We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions (grazing or touching cycle) and the dynamics of the pseudo equilibrium, using quantitative analysis techniques related to nonsmooth Filippov systems. Furthermore, as the threshold value is varied, the model exhibits several complex bifurcations which are classified into equilibria, sliding mode, local sliding (boundary node and focus) and global bifurcations (grazing or touching). In conclusion, we discuss the importance of the refuge strategy in a biological setting.

Regular Equilibria and Negative Welfare Implications in Delegation Games

This study examines delegation games in which each player commits to a reaction function in advance. We focus on the regular subgame perfect equilibria of delegation games in the sense that the chosen reaction functions have an invertible Jacobian. Subsequently we provide a necessary condition under which an action profile is achieved as a regular equilibrium of n-player delegation games. In two-player games with misaligned preferences, each efficient action profile violates the necessary condition. We also show that almost action profiles other than efficient ones are achieved as regular equilibria of the delegation game in which the chosen reaction functions are linear. This finding implies that each delegatee’s objective is written as a quadratic function, which may justify the linear-quadratic specification of the objective functions in applications.

Global Stability of a Non-Smooth Predator–Prey System with Holling I Functional Response and Refuge Effect

This paper analyses the dynamics of a non-smooth predator-prey model with refuge effect, where the functional response is taken as Holling I type. To begin with, some preliminaries and the existence of regular, virtual, pseudo-equilibrium and tangent point are established. Then, the stability of trivial equilibrium and predator free equilibrium is discussed. Furthermore, it is shown that the regular equilibrium and the pseudo-equilibrium cannot coexist. Finally, the conclusion is given.

Determination of Equilibrium Points for Steady State Conservative Models

Determination of Equilibrium Points for Steady State Conservative ModelsThe development and a more sophisticated structure of electric power systems, the transition towards deregulation and competition between the participants of the electric energy market cause the necessity of a complex steady state analysis, the evaluation of the electric power system stability, with its parameters being changed. The paper addresses the steady state analysis based on algebraic methods. Regular (trivial) and non-regular (additional) equilibrium points for the electric power system conservative model are determined. Changing regular and non-regular equilibrium points in a heavily loaded electric power system is studied.

On the branching of equilibrium paths

The local quasi-static behaviour near a compound branching point of a conservative system is analysed. General equations governing the possible regular equilibrium paths through a point where one path is known are derived, in the form of a perturbation sequence appropriate to the data. Among the consequences is an account of the analytical distinctions between smooth and abrupt bifurcations. The theory is immediately applicable to any system (or structure) whose potential energy adequately depends on a finite number of variables.