分枝过程和分枝粒子系统是研究粒子群体在一定的环境下发展演化的数学模型，在分枝过程或分枝粒子系统中加入竞争机制，便得到所谓的带竞争的分枝过程或分枝粒子系统。首先我们将用随机方程分别构造离散状态和连续状态的带竞争的分枝过程的随机流，证明作为轨道值过程，离散的随机流可以收敛到连续的随机流。然后我们用随机方程构造带竞争的分枝粒子系统，研究其灭绝概率并证明其重整化之后会收敛到满足一定鞅问题的带竞争的超过程，最后再证明其满足的鞅问题的解是分布唯一的。

Branching processes and branching particle systems are mathematical models for populations evolving randomly in certain environments. To join the competition in branching processes or branching particle systems, we get the so-called branching processes with competition or branching particle systems with competition. First we will construct the stochastic flows of branching processes with competition by stochastic equations, and establish the convergence of the renormalized discrete-state model to the continuous-state model in the setting of path-valued processes. Then we will use stochastic equations to construct branching particle systems with competition, study their extinction probability and show that after suitable renormalization it can converge to some superprocess with competition, which satisfies some martingale problem. At last we prove this martingale problem has a unique solution.