Developing an evolutionary/ecological approach in enterprise education

This paper presents an ecological/evolutionary approach to enterprise education. Ecological approaches are used at the University of Tasmania to heighten the awareness of students to a raft of difficult to observe environmental factors associated with developing enterprising ideas. At Sheffield University, the discovery and exploitation of entrepreneurial opportunities is viewed as a co-evolving system of emerging business ideas, and routines/heuristics respectively. It is argued that using both approaches enables students to develop a greater awareness of their situated environment, and ultimately the degree of fit between their learning process and a changing external world. The authors argue that in order to improve the chances of longer-term survival what is needed is a new level of organisation where the individual is capable of developing a representation of the external world that he or she can use to sense the appropriateness of local decisions. This reinterpretation of events allows individuals to step back and examine the broader consequences of their actions through the interpretation and anticipation of feedback from the environment. These approaches thus seek to develop practice-based heuristics which individuals can use to make sense of their lived experiences, as they learn to evolve in an increasingly complex world.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.