Java作為一種面向對象的編程語言，繼承和多態是其非常重要的特性之一。在設計動物類時，利用繼承和多態的特性可以讓代碼更加簡潔、易讀，同時也提高了代碼的可擴展性和重用性。

我們可以首先定義一個Animal類，然后創建幾個子類比如Cat，Dog和Bird。其中Animal類定義了一系列的共同特征和操作，如呼吸、進食等，而各個子類又擁有自身獨特的特征和操作。

public class Animal {
private String name;
private int age;
// Constructor
public Animal(String name, int age) {
this.name = name;
this.age = age;
}
// Getter and Setter methods
public String getName() {
return name;
}
public void setName(String name) {
this.name = name;
}
public int getAge() {
return age;
}
public void setAge(int age) {
this.age = age;
}
// Common behaviors of animals
public void breathe() {
System.out.println(this.name + " is breathing.");
}
public void eat() {
System.out.println(this.name + " is eating.");
}
}
public class Cat extends Animal{
private String coatColor;
// Constructor
public Cat(String name, int age, String coatColor) {
super(name, age);
this.coatColor = coatColor;
}
// Getter and Setter method
public String getCoatColor() {
return coatColor;
}
public void setCoatColor(String coatColor) {
this.coatColor = coatColor;
}
// Unique behavior of cat
public void meow() {
System.out.println(this.getName() + " is meowing.");
}
}
public class Dog extends Animal{
private String breed;
// Constructor
public Dog(String name, int age, String breed) {
super(name, age);
this.breed = breed;
}
// Getter and Setter method
public String getBreed() {
return breed;
}
public void setBreed(String breed) {
this.breed = breed;
}
// Unique behavior of dog
public void bark() {
System.out.println(this.getName() + " is barking.");
}
}
public class Bird extends Animal{
private String featherColor;
// Constructor
public Bird(String name, int age, String featherColor) {
super(name, age);
this.featherColor = featherColor;
}
// Getter and Setter method
public String getFeatherColor() {
return featherColor;
}
public void setFeatherColor(String featherColor) {
this.featherColor = featherColor;
}
// Unique behavior of bird
public void fly() {
System.out.println(this.getName() + " is flying.");
}
}

在使用繼承和多態的時候，我們可以聲明一個Animal類型的引用變量，并將其指向Cat，Dog或者Bird的對象，從而使得這個引用變量可以執行相應的方法。這樣做有很多好處，比如可以降低代碼的復雜度，提高代碼的可讀性。

public static void main(String[] args) {
Animal cat = new Cat("Tom", 3, "gray");
Animal dog = new Dog("Spike", 2, "Bulldog");
Animal bird = new Bird("Tweety", 1, "yellow");
// Calling common behaviors of animals
cat.breathe();
dog.eat();
bird.eat();
// Calling unique behaviors
if(cat instanceof Cat) {
((Cat) cat).meow();
}
if(dog instanceof Dog) {
((Dog) dog).bark();
}
if(bird instanceof Bird) {
((Bird) bird).fly();
}
}

通過運行上面的程序，我們可以看到貓、狗和鳥分別執行了它們自己的獨特方法，同時也能夠呼吸和進食。這就是繼承和多態的好處所在。