Abstract: Systems, methods, apparatus, and techniques are presented for maintaining cupolets in a state of mutual stabilization. A first cupolet and a second cupolet are generated. A first control code is applied to the first cupolet for a first time to produce a first visitation code. The first visitation code is transformed based on an exchange function to produce a second control code. The second control code is applied to the second cupolet to produce a second visitation code. The second visitation code is transformed based on the exchange function to produce the first control code. The first control code is applied to the first cupolet for a second time.

Abstract: A method includes receiving an input signal comprising an original domain signal and creating a first window data set and a second window data set from the signal, wherein an initiation of the second window data set is offset from an initiation of the first window data set, converting the first window data set and the second window data set to a frequency domain and storing the resulting data as data in a second domain different from the original domain, performing complex spectral phase evolution (CSPE) on the second domain data to estimate component frequencies of the first and second window data sets, using the component frequencies estimated in the CSPE, sampling a set of second-domain high resolution windows to select a mathematical representation comprising a second-domain high resolution window that fits at least one of the amplitude, phase, amplitude modulation and frequency modulation of a component of an underlying signal wherein the component comprises at least one oscillator peak, generating an ou

Abstract: A method of processing a signal, including taking a signal formed from a plurality of source signal emitters and expressed in an original domain, decomposing the signal into a mathematical representation of a plurality of constituent elements in an alternate domain, analyzing the plurality of constituent elements to associate at least a subset of the constituent elements with at least one of the plurality of source signal emitters, separating at least a subset of the constituent elements based on the association and reconstituting at least a subset of constituent elements to produce an output signal in at least one of the original domain, the alternate domain and another domain.

Abstract: A method of processing a signal, including taking a signal formed from a plurality of source signal emitters and expressed in an original domain, decomposing the signal into a mathematical representation of a plurality of constituent elements in an alternate domain, analyzing the plurality of constituent elements to associate at least a subset of the constituent elements with at least one of the plurality of source signal emitters, separating at least a subset of the constituent elements based on the association and reconstituting at least a subset of constituent elements to produce an output signal in at least one of the original domain, the alternate domain and another domain.

Abstract: A method of processing a signal, including taking a signal formed from a plurality of source signal emitters and expressed in an original domain, decomposing the signal into a mathematical representation of a plurality of constituent elements in an alternate domain, analyzing the plurality of constituent elements to associate at least a subset of the constituent elements with at least one of the plurality of source signal emitters, separating at least a subset of the constituent elements based on the association and reconstituting at least a subset of constituent elements to produce an output signal in at least one of the original domain, the alternate domain and another domain.

Abstract: Systems and methods for signal analysis using orbits of a chaotic system are provided. For example, a multiresolution analysis may be constructed and cupolets may be used to approximate arbitrary signals and compress images. Cupolets may be phase transformed to produce compact cupolets that are well-suited for producing sharp changes in signals, or to produce compact cupolets that are more oscillatory and have less or no sharp global maximum amplitudes. Alternatively, cupolets may be phase transformed to allow for optimal or near optimal adjustment to fit a signal.

Abstract: A method and apparatus that uses tha dynamics of chaotic system for the remote generation of a digital key, for use in any encryption algorithm. After initialization, the dynamics of a chaotic system are allowed to generate the 0 and 1 bits of a key bistream. An initialization bistream is transmitted, using conventional transmission technologies, to an identical chaotic system. This chaotic system is driven into synchrony and allow to generate a key bitsream, which is identical to the other bitstream because the chaotic systems have been sychronized.

Abstract: Systems and methods for signal analysis using orbits of a chaotic system are provided. For example, a multiresolution analysis may be constructed and cupolets may be used to approximate arbitrary signals and compress images. Cupolets may be phase transformed to produce compact cupolets that are well-suited for producing sharp changes in signals, or to produce compact cupolets that are more oscillatory and have less or no sharp global maximum amplitudes. Alternatively, cupolets may be phase transformed to allow for optimal or near optimal adjustment to fit a signal.

Abstract: The present invention is a compression method for compressing digital data. The data is strings of digital values, which can be broken down to a series of 1's and 0's. The present inventive method uses a chaotic system to compress the data. The first step in the inventive method is generating a plurality of periodic orbits that correspond to a plurality of control bit strings. Each of the periodic orbits is formed with a series of numeric values. The next step is to convert the numeric values of the periodic orbits to digital data values, similar in form to the data to be compressed. The digital data values of the periodic orbits are then organized to identically match the original digital data values. Then the control bit strings corresponding to the organized digital data values of the periodic orbits are identified and saved in order, such that applying the control bit strings to the chaotic system will regenerate the original data.

Abstract: A method and apparatus that uses the dynamics of chaotic systems for the remote generation of a digital key, for use in any encryption algorithm. After initialization, the dynamics of a chaotic system are allowed to generate the 0 and 1 bits of a key bitstream. An initialization bitstream is transmitted, using conventional transmission technologies, to an identical chaotic system. This chaotic system is driven into synchrony and allowed to generate a key bitstream, which is identical to the other bitstream because the chaotic systems have been synchronized.

Abstract: A system for the compression and decompression of sections of audio files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of the selected basic waveforms is used to approximate a section of audio file. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed audio file. When the compressed audio file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to reproduce the original section of audio file.

Abstract: A system for the compression and decompression of image files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of selected basic waveforms is used to approximate each slice of an image. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed image file. When the compressed image file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to produce an approximation of the original image slice.

Abstract: A system for the compression and decompression of image files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of selected basic waveforms is used to approximate each slice of an image. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed image file. When the compressed image file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to produce an approximation of the original image slice.

Abstract: A method and apparatus that uses the dynamics of chaotic systems for the remote generation of a digital key, for use in any encryption algorithm. After initialization, the dynamics of a chaotic system are allowed to generate the 0 and 1 bits of a key bitstream. An initialization bitstream is transmitted, using conventional transmission technologies, to an identical chaotic system. This chaotic system is driven into synchrony and allowed to generate a key bitstream, which is identical to the other bitstream because the chaotic systems have been synchronized.

Abstract: The present invention is a compression method for compressing digital data. The data is strings of digital values, which can be broken down to a series of 1's and 0's. The present inventive method uses a chaotic system to compress the data. The first step in the inventive method is generating a plurality of periodic orbits that correspond to a plurality of control bit strings. Each of the periodic orbits is formed with a series of numeric values. The next step is to convert the numeric values of the periodic orbits to digital data values, similar in form to the data to be compressed. The digital data values of the periodic orbits are then organized to identically match the original digital data values. Then the control bit strings corresponding to the organized digital data values of the periodic orbits are identified and saved in order, such that applying the control bit strings to the chaotic system will regenerate the original data.

Abstract: A method and apparatus that uses control of a chaotic system to produce secure digital chaotic communication. Controls are intermittently applied by a transmitter-encoder to a chaotic system to generate the 0 and 1 bits of a digital message. A new control/no control bit stream is thereby created in which a 0 indicates that no control was applied and a 1 indicates that a control was applied. The control/no control bit stream and a prepended synchronization bit stream are transmitted, using conventional transmission technologies, from the transmitter-encoder to an identical receiver-decoder. A chaotic system in the receiver-decoder is driven into synchrony and is subject to intermittent controls based on the control/no control bit stream, thereby causing it to generate the digital message.

Abstract: A new method and apparatus for music synthesis is provided. A chaotic system is driven onto a periodic orbit by a compressed initialization code. A one-dimensional, periodic waveform is then produced from the periodic orbit. A variety of periodic orbits produces a variety of sounds, which sounds approximate the sounds of different musical instruments. By sampling the amplitude of the periodic waveforms over time, a digital version of the sound is produced. The frequency and duration of a note to be synthesized are produced by sampling the periodic waveform at the proper rate to produce the desired frequency and then repeating the waveform to produce a note of the required duration.