R中参数随时间变化的微分方程组的图解

# 安装和加载必要的包
install.packages("deSolve")
install.packages("ggplot2")
library(deSolve)
library(ggplot2)

# 定义微分方程组
equations <- function(time, state, parameters) {
  with(as.list(c(state, parameters)), {
    # 定义微分方程
    dX <- r * X - a * X * Y
    dY <- -s * Y + b * X * Y
    
    # 返回微分方程组的结果
    return(list(c(dX, dY)))
  })
}

# 定义参数和初始条件
parameters <- c(r = 0.1, a = 0.02, s = 0.1, b = 0.01)
initial_state <- c(X = 10, Y = 5)

# 求解微分方程组
solution <- ode(y = initial_state, times = seq(0, 100, by = 0.1), func = equations, parms = parameters)

# 将解转换为数据框
solution_df <- as.data.frame(solution)

# 绘制解随时间变化的曲线图
ggplot(data = solution_df, aes(x = time)) +
  geom_line(aes(y = X, color = "X")) +
  geom_line(aes(y = Y, color = "Y")) +
  labs(x = "Time", y = "Value", color = "Variable") +
  theme_minimal()