The behavior of army ants at each environment as shown in Table 1 was observed. Parameter settings are as follows: n=2, a=0.4, and r
e
=0.05. At each environment in this paper, 10 trials for each set were executed and the behavior of ants were recorded as the motion video. There are 2 kinds of ants at each environment, Major ants to make a random search and Minor ants to follow the scattered pheromone. In this paper, for almost trials we can observe the following simulation results. During the initial phase as the search of an area for prey, the movement of Major agent will be a key in the change of course to search the subspace, because the Major agent scatters the pheromone while moving in a space. After the discovery of food, the Minor agent catches the food and scatters the pheromone on the way from the spot to the nest. The path becomes congested since there is an obstacle of a ditch. Such situation causes the construction of the bridge on the ditch, since the ants search the shortest path from the feeding spot to the nest. Moreover, the agent swarming around the food increases with the size of food, because more pheromone is scattered while the agent brings a food to the nest. That is, the larger the food in the environment has, the more pheromone the agents scattered.
Transition of 100 agents
Figures 7 show the number of agents in each area, A, B, and C, with 100 agents in the environment. In case of 100 agents, they are divided into some groups and each group can search the area, respectively. Figure 7(A), Figure 7(B), Figure 7(C), and Figure 7(D) show the transition of agents with A:B:C={2:1:1, 1:2:1, 1:1:2, 4:2:1}, respectively. The transition of agents as shown in these figures emerged 7 or 8 times of 10 trials in each situation. We can observe that ant agents carry the food from the nearest food spot or the largest size of food spot. Note that even if the food size of area A is the largest, the food of area A remains until area B or area C is disappeared. Because ant agents find areas B or C and bring all food from area B or area C, respectively.
On the contrary, Figure 7(C) (A:B:C=1:1:2), Figure 8(A) (A:B:C=2:1:1), and Figure 8(B) show that the results are beyond our expectations. In the experiment as to Figure 7(C), more agents gathered to the areas B and C than the area A at the initial phase. And then agents moved to area C larger than area B and they made a bridge in the area C. After the food was lost in area C, the ants in area C moved to area A. We expected area B than area A will be disappeared, because some agents visited area B and they knew the existence of area B. However, most agents moved to A, because the pheromone at the initial phase was disappeared. Therefore, the food of B was carried to the nest after area A was lost.
In the experiment as to Figure 8(A), agents gathered to area B too much. As a result, the wide bridge was constructed between area B and the nest. Because almost agents were in altruism state and only a few agents could carry the food to the nest, it took a long time to finish the work in area B and they could not proceed to the area A. Some agents in area B moved to area C according to pheromone scattered by Major ants. After the agents finished the work in area C, they could move to area A at last. When ant agents concentrated superfluously, the search might not progress.
In the experiment as to Figure 8(B), agents gathered to area B and the bridge between area B and the nest was constructed. Some agents in area B were attracted by the largest size of area A. As a result, because there were not almost agents in area C, the bridge was not constructed in area C and the agents avoided the ditch to carry the food.
We summary the characteristic behaviors under the 100 agents as follows.
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1.
Most agents gather to the left area and the right area near from the nest. They move to the bottom area after they finish the work at each area.
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2.
Pheromone scattered by Major agents attracts the minor agents and they move to one of the left area and the right area. They move to the bottom area after they finished the work at the area.
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3.
Some agents make a bridge on the way from the nest to the food spot.
Transition of 50 agents
Figures 9 show the number of agents in each area, A, B, and C, with 50 agents in the environment. The situation has 50 agents in the environment, they cannot search the space sufficiently. The ants did not divide into some search group and then the search of area was processed sequentially such as A→B→C. Figure 9(A) and Figure 9(D) show the transition of agents in case of A:B:C={2:1:1,4:2:1}, respectively. As shown in these figures, we can observe general behaviors in the search space. That is, the feeding spots are disappeared in the order of larger spot. On the contrary, Figure 9(B) (A:B:C=1:2:1) and Figure 9(C) (A:B:C=1:1:2) show that the result is beyond our expectations. In case of Figure 9(B), the constructed bridges were not in the shortest path on the way to the nest as shown in Figure 8(B). In case of Figure 9(B), it is an interesting case, and almost agents will make bridges place to place in the ditch from area C to the nest. The remaining agents should deliver the food to the nest, however very few agents cannot take all of them. The scattered pheromone was smaller than the evaporated pheromone. Therefore, the pheromone around the bridge disappears and then the bridge was destroyed, because the agents in altruism situation depart the bridge in the condition of less pheromone. The agent leaving from the bridge moves to area A, but there are only a few agents in the area. From such results, only few agents in the environment with large size of food cannot get the altruism situation easily.
We summary the characteristic behaviors under the 50 agents as follows.
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1.
Most agents gather to the left area and the right area near from the nest. They move to the bottom area after they finish the work at each area.
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2.
If the food size is the largest in the bottom area, the agents gather there regardless of the distance from the food spot to the nest. They separate to move the remaining spot after they finish the work at the area (See Additional file 1).