The present invention relates to a fuel supply apparatus and an air-fuel ratio control system for an internal combustion engine. More particularly, the invention relates to a fuel supply apparatus and an air-fuel ratio control system in which fuel is atomized in response to the output from a fuel injection valve provided on each of the cylinders of an internal combustion engine. An apparatus of this type is disclosed in Japanese Patent Publication No. 56-1376. According to this apparatus, a fuel injection valve is provided on each cylinder of an internal combustion engine for injecting fuel into the combustion chamber of each cylinder. The fuel injection valve is connected to an engine control unit through a common signal line so as to be able to control the timing, the period and the amount of fuel injection in response to the signal sent from the engine control unit. Each fuel injection valve is provided with a signal detector for detecting the value of the output from an accelerator opening sensor. When the accelerator opening sensor detects a degree of opening greater than the predetermined value, the fuel injection valves inject fuel according to the predetermined injection patterns in which the time periods of fuel injection and the amounts of fuel to be injected are increased. When the degree of opening of the accelerator is lower than the predetermined value, on the other hand, the fuel injection valves inject fuel according to another predetermined injection pattern in which the time period of fuel injection and the amount of fuel to be injected are decreased. Each injection pattern corresponds to a lean running state in which the ratio between the air and the fuel is controlled so that a satisfactory power can be obtained, and to a rich running state in which the ratio between the air and the fuel is controlled so that exhaust gas can be cleaned by a three-way catalyst. The output signals from the signal detector in the individual fuel injection valves are also sent to the engine control unit through the common signal line. In response to these output signals, the engine control unit determines whether the running condition of the engine is a lean running state or a rich running state. The engine control unit then causes the fuel injection valves to inject fuel in accordance with the determined running state. Each fuel injection valve is provided with a fuel flow rate detector for detecting the flow rate of fuel. When the engine is running in the lean running state, the engine control unit causes the fuel injection valves to inject fuel so as to make the air-fuel ratio of the mixture fed into the combustion chambers of the cylinders equal to a target value which is determined in accordance with the running state of the engine. When the engine is running in the rich running state, on the other hand, the engine control unit causes the fuel injection valves to inject fuel so as to increase the air-fuel ratio. That is, the engine control unit determines the amounts of fuel to be injected by the fuel injection valves in accordance with both of the output signals from the signal detector and the flow rate detector in each fuel injection valve. The engine control unit then causes the fuel injection valves to inject fuel so as to make the air-fuel ratio in the cylinder equal to the target value. However, it is necessary to increase the capacity of the fuel supply apparatus as the number of engine cylinders is increased. It is also necessary to increase the capacity of the fuel supply apparatus when an increased amount of fuel is required as the running condition is changed from a lean running state to a rich running state. Therefore, it is difficult to reduce the size of the apparatus, and it is also difficult to reduce the cost of manufacture. In a modern diesel engine, fuel is atomized by injecting fuel into the combustion chamber of a cylinder during an intake stroke so that the fuel can be satisfactorily mixed with air in the combustion chamber. Therefore, a certain amount of time must be allowed from the start of fuel injection until the completion of fuel injection for mixing fuel with air in the combustion chamber. When the running condition of the engine changes from a lean running state to a rich running state, on the other hand, the engine control unit controls the time period during which fuel is injected in accordance with the output signals from the signal detector. Consequently, it is not possible to start the fuel injection until a predetermined time elapses after the start of fuel injection. In other words, the engine control unit is not able to control the amount of fuel to be injected in accordance with both of the time period during which fuel is injected and the signal which indicates the running condition of the engine. Therefore, it is not possible to control the air-fuel ratio so that the air-fuel ratio matches the target value. The air-fuel ratio is changed so as to become lower than the target value. This causes exhaust gas to flow through the three-way catalyst so that pollution of the atmosphere increases. As described above, it is necessary to increase the capacity of the fuel supply apparatus so as to increase the size of the fuel supply apparatus as the number of engine cylinders is increased. Therefore, it is not possible to reduce the size of the fuel supply apparatus. In addition, it is not possible to reduce the manufacturing cost of the fuel supply apparatus. Japanese Patent Application Laid-open No. 1-225,748 discloses a fuel supply apparatus which is arranged such that an air-fuel ratio is prevented from being changed so as to deviate from the target value, while preventing over-correction so as to enhance the response to a fuel-increase command which is delivered to the fuel supply apparatus during a rich running state. In this apparatus, however, an optimal fuel-increase correction amount, i.e., a fuel increase correction amount which optimizes a change of the air-fuel ratio to the rich direction from the target value, changes depending upon the running state of the engine. Therefore, it is not possible to control the air-fuel ratio to the target value by a single fuel-increase correction amount during the rich running state. For this reason, the apparatus must be provided with a corresponding number of optimal fuel-increase correction amounts as needed. In addition, it is not possible to set a predetermined fuel increase correction amount for a particular running state in which a running condition of the engine is the same as that of another running condition. As a result, it is necessary to set different fuel increase correction amounts for different running states. This causes the size of the fuel supply apparatus to be increased. The air-fuel ratio control systems disclosed in Japanese Utility Model Application Laid-open No. 2-14,747 and in Japanese Patent Application Laid-open No. 61-59,754 also increase the size of the fuel supply apparatus as the number of engine cylinders is increased. In the former system, an airflow meter and a water temperature sensor are provided on each intake passage. An air-fuel ratio sensor is provided on the exhaust passage. An engine control unit calculates a target air-fuel ratio according to a signal which indicates the running condition of the engine from the signals supplied from the airflow meter and the water temperature sensor. The engine control unit then controls the air-fuel ratio so that the air-fuel ratio equals the target value. The fuel supply apparatus is provided with first to third air flow rate regulating means, and fuel flow rate setting means. When it is determined that the engine is running in a rich running state, on the other hand, the fuel flow rate setting means increases the ratio between the air flow rate and the fuel flow rate, that is, the fuel injection ratio, as compared with when the engine is running in a lean running state. In the latter system, however, the first, second and third airflow control means, and the first, second and third means for setting the airflow rate are connected in parallel between the airflow passage and the air-fuel ratio sensor. When the running condition of the engine changes from a lean running state to a rich running state, therefore, the amount of air which flows through the third airflow control means increases in response to a large amount of fuel injection from the fuel injection valve. This results in a change in the output of the air-fuel ratio sensor. The air-fuel ratio control system disclosed in Japanese Patent Application Laid-open No. 3-76,831 is arranged so as to avoid this problem. This system is provided with an airflow meter and an oxygen detector, on each intake passage. A throttle valve is arranged in the intake passage on the downstream side of the airflow meter. A fuel injection valve is provided on each of the intake passages. The fuel injection valve is used for injecting fuel into the intake passage during each of the intake strokes of the engine. The fuel injection valves inject fuel so as to set the air-fuel ratio of the mixture at a predetermined value which is selected in accordance with the running condition of the engine. The engine control unit sends a control signal which indicates a fuel injection control amount to the fuel injection valve of each intake passage through a single signal line. A signal generator generates an output signal which indicates the running state of the engine in response to the rotational speed of the engine and a temperature signal which is detected by a temperature sensor. The fuel flow rate detector detects the flow rate of fuel from each fuel injection valve. A first comparison means compares the output of the airflow meter with a predetermined reference value and generates a first signal when the airflow meter indicates an airflow value which is lower than the predetermined reference value. A second comparison means compares the output of the oxygen detector with a predetermined reference value and generates a second signal when the oxygen detector indicates an oxygen value which is higher than the predetermined reference value. A throttle opening detection means detects the degree of opening