Method for synchronizing a plurality of chaotic systems and method for multichannel communication using synchronized chaotic systems

A vertical synchronizing method for successively synchronizing a plurality of chaotic systems, each chaotic system having a master chaotic device and a slave chaotic device identical to the master chaotic device, comprising the steps of:

• synchronizing first chaotic system having first master chaotic device and first slave chaotic device wherein at least one parameter of the first master chaotic device is modulated by a noise signal, and at least one parameter of the first slave chaotic device which corresponds to the parameter of the first master chaotic device is modulated by the noise signal;
• synchronizing second chaotic system having second master chaotic device and second slave chaotic device wherein at least one parameter of the second master chaotic device is modulated by an arbitrary variable signal of the first master chaotic device, and at least one parameter of the second slave device which corresponds to the parameter of the second master device is modulated by an arbitrary variable signal of the first slave chaotic device which corresponds the arbitrary variable signal of the first slave chaotic device;
• and
• synchronizing ith chaotic system having ith master chaotic device and ith slave chaotic device wherein at least one parameter of the ith master chaotic device is modulated by an arbitrary variable signal of i-lth master chaotic, and at least one parameter of the ith slave device which corresponds to the parameter of the ith master device is modulated by an arbitrary variable signal of i-lth slave chaotic device which corresponds the arbitrary variable signal of i-lth master chaotic device where i equals 3 to N of number of the chaotic systems.

A horizontal synchronizing method for synchronizing a plurality of inferior chaotic systems which are horizontally independent and a superior chaotic system, comprising the steps of:

• synchronizing first inferior chaotic system having first master chaotic device and first slave chaotic device wherein first variable among a plurality of variables of a master chaotic device of the superior chaotic system is added to at least one variable of the first master chaotic device of the first inferior chaotic system, and first variable of a slave chaotic device of the superior chaotic system which corresponds to the first variable of the master chaotic device of the superior chaotic system is added to at least one variable of the first slave chaotic device of the first inferior chaotic system;
• synchronizing second inferior chaotic system having second master chaotic device and second slave chaotic device wherein second variable among the plurality of variables of the master chaotic device of the superior chaotic system is added to at least one variable of the second master chaotic device of the second inferior chaotic system, and second variable of the slave chaotic device of the superior chaotic system which corresponds to the second variable of the master chaotic device of the superior chaotic system is added to at least one variable of the second slave chaotic device of the second inferior chaotic system;
• and
• synchronizing ith inferior chaotic system having ith master chaotic device and ith slave chaotic device wherein ith variable among the plurality of variables of the master chaotic device of the superior chaotic system is added to at least one variable of the ith master chaotic device of the ith inferior chaotic system, and ith variable of the slave chaotic device of the superior chaotic system which corresponds to the ith variable of the master chaotic device of the superior chaotic system is added to at least one variable of the ith slave chaotic device of the ith inferior chaotic system where i equals 3 to N of number of the inferior chaotic systems.

A horizontal synchronizing method for synchronizing a plurality of inferior chaotic systems which are horizontally independent and a superior chaotic system, comprising the steps of:

• synchronizing first inferior chaotic system having first master chaotic device and first slave chaotic device wherein at least one parameter of the first master chaotic device of the first inferior chaotic system is modulated by first variable among a plurality of variables of a master chaotic device of the superior chaotic system, and at least one parameter of the first slave chaotic device of the first inferior chaotic system is modulated by first variable of a slave chaotic device of the superior chaotic system which corresponds to the first variable of the master chaotic device of the superior chaotic system;
• synchronizing second inferior chaotic system having second master chaotic device and second slave chaotic device wherein at least one parameter of the second master chaotic device of the second inferior chaotic system is modulated by second variable among the plurality of variables of the master chaotic device of the superior chaotic system, and at least one parameter of the second slave chaotic device of the second inferior chaotic system is modulated by second variable of the slave chaotic device of the superior chaotic system which corresponds to the second variable of the master chaotic device of the superior chaotic system;
• and
• synchronizing ith inferior chaotic system having ith master chaotic device and ith slave chaotic device wherein at least one parameter of the ith master chaotic device of the ith inferior chaotic system is modulated by ith variable among the plurality of variables of the master chaotic device of the superior chaotic system, and at least one parameter of the ith slave chaotic device of the ith inferior chaotic system is modulated by ith variable of the slave chaotic device of the superior chaotic system which corresponds to the ith variable of the master chaotic device of the superior chaotic system where i equals to 3 to N of number of the inferior chaotic systems.

A method for multichannel secure communication by successively synchronizing a plurality of chaotic systems, each chaotic system having a master chaotic device and a slave chaotic device identical to the master chaotic device, comprising the steps of:

• synchronizing first chaotic system having first master chaotic device and first slave chaotic device wherein a noise signal is added to at least one variable of the first master chaotic device, and the noise signal is added to at least one variable of the first slave chaotic device which corresponds to the variable of the first master chaotic device;
• synchronizing second chaotic system having second master chaotic device and second slave chaotic device wherein an arbitrary variable signal of the first master chaotic device is added to at least one variable of the second master chaotic device, and an arbitrary variable signal of the first slave chaotic device which corresponds the arbitrary variable signal of the first slave chaotic device is added to at least one variable of the second slave device which corresponds to the variable of the second master device;
• and
• synchronizing ith chaotic system having ith master chaotic device and ith slave chaotic device wherein an arbitrary variable signal of i-lth master chaotic device is added to at least one variable of the ith master chaotic device, and an arbitrary variable signal of i-lth slave chaotic device which corresponds the arbitrary variable signal of i-lth master chaotic device is added to at least one variable of the ith slave chaotic device which corresponds to the variable of the ith master device where i equals 3 to N of number of the chaotic systems;
• and
• transmitting each masked signal including each message signal and each chaotic signal generated from each master chaotic device of each synchronized chaotic system, and retrieving each message signal by removing each chaotic signal of each slave chaotic device which corresponds to each chaotic signal of each master chaotic device of each synchronized chaotic system from each masked signal.

A method for multichannel secure communication by successively synchronizing a plurality of chaotic systems, each chaotic system having a master chaotic device and a slave chaotic device identical to the master chaotic device, comprising the steps of:

• synchronizing first chaotic system having first master chaotic device and first slave chaotic device wherein at least one parameter of the first master chaotic device is modulated by a noise signal, and at least one parameter of the first slave chaotic device which corresponds to the parameter of the first master chaotic device is modulated by the noise signal;
• synchronizing second chaotic system having second master chaotic device and second slave chaotic device wherein at least one parameter of the second master chaotic device is modulated by an arbitrary variable signal of the first master chaotic device, and at least one parameter of the second slave device which corresponds to the parameter of the second master device is modulated by an arbitrary variable signal of the first slave chaotic device which corresponds the arbitrary variable signal of the first slave chaotic device;
• and
• synchronizing ith chaotic system having ith master chaotic device and ith slave chaotic device wherein at least one parameter of the ith master chaotic device is modulated by an arbitrary variable signal of i-lth master chaotic, and at least one parameter of the ith slave device which corresponds to the parameter of the ith master device is modulated by an arbitrary variable signal of i-lth slave chaotic device which corresponds the arbitrary variable signal of i-lth master chaotic device where i equals 3 to N of number of the chaotic systems;
• and
• transmitting each masked signal including each message signal and each chaotic signal generated from each master chaotic device of each synchronized chaotic system, and retrieving each message signal by removing each chaotic signal of each slave chaotic device which corresponds to each chaotic signal of each master chaotic device of each synchronized chaotic system from each masked signal.