One simple possibility would be $$x_n(t+1)=x_n(t)-\mu(x_m(t)-x_n(t))^{-\gamma}\cdot x_n(t)\cdot (1-x_n(t))$$

• The minus sign before $\mu$ makes the interaction repulsive.
• $\gamma$ makes the repulsion smaller as the agents are further away with $\gamma>1$.
• The $x_n(t)$ makes the repulsion smaller as $x_n$ becomes closer to the left boundary
• The $(1-x_n(t))$ term makes the repulsion smaller as $x_n$ becomes closer to the right boundary
• Since the agents are always in the interval [0,1] the signs of $x_n,(1-x_n)$ are always correct
• A different range of $\mu$ would have to be chosen to account for these additional factors

This force becomes larger in the middle $x_n\approx 1/2$ which is hard to avoid when you want to keep the agents inside [0,1]. You can take different powers of $x_n, (1-x_n)$ to make this effect less noticable. For example $x_n^{1/4}$ and $(1-x_n)^{1/4}$ where 4 could be any number.

One simple possibility would be $$x_n(t+1)=x_n(t)-\mu\cdot\text{ sgn}(x_m(t)-x_n(t))\cdot|x_m(t)-x_n(t)|^{-\gamma}\cdot x_n(t)\cdot (1-x_n(t))$$

• The minus sign before $\mu$ makes the interaction repulsive.
• $\gamma$ makes the repulsion smaller as the agents get further away if $\gamma>1$.
• The $x_n(t)$ makes the repulsion smaller as $x_n$ becomes closer to the left boundary
• The $(1-x_n(t))$ term makes the repulsion smaller as $x_n$ becomes closer to the right boundary
• Since the agents are always in the interval [0,1] the signs of $x_n,(1-x_n)$ are always correct
• A different range of $\mu$ would have to be chosen to account for these additional factors

This force becomes larger in the middle $x_n\approx 1/2$ which is hard to avoid when you want to keep the agents inside [0,1]. You can take different powers of $x_n, (1-x_n)$ to make this effect less noticable. For example $x_n^{1/4}$ and $(1-x_n)^{1/4}$ where 4 could be any number.

One simple possibility would be $$x_n(t+1)=x_n(t)-\mu(x_m(t)-x_n(t))\cdot x_n(t)\cdot (1-x_n(t))$$

• The minus sign before $\mu$ makes the interaction repulsive.
• The $x_n(t)$ makes the repulsion smaller as $x_n$ becomes closer to the left boundary
• The $(1-x_n(t))$ term makes the repulsion smaller as $x_n$ becomes closer to the right boundary
• Since the agents are always in the interval [0,1] the signs of $x_n,(1-x_n)$ are always correct
• A different range of $\mu$ would have to be chosen to account for these additional factors

This force becomes larger in the middle $x_n\approx 1/2$ which is hard to avoid when you want to keep the agents inside [0,1]. You can take different powers of $x_n, (1-x_n)$ to make this effect less noticable. For example $x_n^{1/4}$ and $(1-x_n)^{1/4}$ where 4 could be any number.

One simple possibility would be $$x_n(t+1)=x_n(t)-\mu(x_m(t)-x_n(t))^{-\gamma}\cdot x_n(t)\cdot (1-x_n(t))$$

• The minus sign before $\mu$ makes the interaction repulsive.
• $\gamma$ makes the repulsion smaller as the agents are further away with $\gamma>1$.
• The $x_n(t)$ makes the repulsion smaller as $x_n$ becomes closer to the left boundary
• The $(1-x_n(t))$ term makes the repulsion smaller as $x_n$ becomes closer to the right boundary
• Since the agents are always in the interval [0,1] the signs of $x_n,(1-x_n)$ are always correct
• A different range of $\mu$ would have to be chosen to account for these additional factors

This force becomes larger in the middle $x_n\approx 1/2$ which is hard to avoid when you want to keep the agents inside [0,1]. You can take different powers of $x_n, (1-x_n)$ to make this effect less noticable. For example $x_n^{1/4}$ and $(1-x_n)^{1/4}$ where 4 could be any number.