摘要
研究了一类具有稀疏效应的Volterra模型的动力性态.分析发现,系统最多有3个平衡点.用规范形研究表明,在不同的参数范围下,这3个平衡点可以是鞍点、稳定结点、不稳定的结点、鞍结点和弱中心.利用第一Lyapunov系数方法,证明了系统在弱中心附近发生超临界Hopf分支,并在弱中心附近分支出唯一的极限环;利用Poincare-Bendison定理,证明了系统在不稳定平衡点时,总存在极限环.
The dynamical behaviors a Volterra model with sparse effect are discussed. The system is to have three equilibrium points at most. By the normal form theory, these equilibrium points may shown be sad- dle point,stable node,unstable node,saddle-node or weak center, depending on the ranges of parameters. By using the first Lyapunov number,it is proved that the system undergoes a supercritical Hopf bifurcation and hence a unique stable limit cycle occurs. By using the Poincare-Bendison theorem, it is proved that the system always has a limit cycle when it has an unstable equilibrium.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第6期10-14,共5页
Journal of Southwest China Normal University(Natural Science Edition)
基金
中央高校基金资助项目(CDJXS11100027)
关键词
稀疏效应
平衡点
弱中心
HOPF分支
sparse effect
equilibrium point
weak center
Hopf bifurcation
