Chaos: An Interdisciplinary Journal of Nonlinear Science
This paper reports the first finding of cupolets in a chaotic Hindmarsh–Rose neural model. Cupole... more This paper reports the first finding of cupolets in a chaotic Hindmarsh–Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh–Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function rN(x). We report the discovery of many cupolets with...
Recent work has highlighted the vast array of dynamics possible within both neuronal networks and... more Recent work has highlighted the vast array of dynamics possible within both neuronal networks and individual neural models. In this work, we demonstrate the capability of interacting chaotic Hindmarsh–Rose neurons to communicate and transition into periodic dynamics through specific interactions which we call mutual stabilization, despite individual units existing in chaotic parameter regimes. Mutual stabilization has been seen before in other chaotic systems but has yet to be reported in interacting neural models. The process of chaotic stabilization is similar to related previous work, where a control scheme which provides small perturbations on carefully chosen Poincaré surfaces that act as control planes stabilized a chaotic trajectory onto a cupolet. For mutual stabilization to occur, the symbolic dynamics of a cupolet are passed through an interaction function such that the output acts as a control on a second chaotic system. If chosen correctly, the second system stabilizes o...
Benefits of interdisciplinary student participation in a university's entrepreneurial activities ... more Benefits of interdisciplinary student participation in a university's entrepreneurial activities are well known. Still, institutional barriers (structural, temporal, spatial, economic, attitudinal) conspire to block participation. Aided by the NSF's Pathways to Innovation Program, the authors conducted a field experiment to increase STEM student participation in a high-profile business proposal competition (BPC). The experiment employed two interventions: informal social networks and bricolage-the innovative and parsimonious use of existing resources. Utilizing these interventions, the authors collaborated to innovatively exploit the Business College's BPC and Engineering College's capstone engineering projects course (CEP). The goal was to facilitate and track STEM students' BPC participation. Participation was voluntary, and not graded. Participation in the BPC increased from 10 STEM students to 27 and the number of BPC finalists increased from 1 STEM-business interdisciplinary team to 4 following the intervention. Findings demonstrate that social network and bricolage-inspired intervention appear useful in increasing STEM student and interdisciplinary team BPC participation and success.
We consider the quantum-classical correspondence from a classical perspective by discussing the p... more We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system's set of cupolets, which are essentially highly-accurate stabilizations of its unstable periodic orbits. The discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external intervention. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. In this paper, we further describe chaotic entanglement and go on to discuss the capacity for chaotic systems to exhibit other characteristic...
This paper discusses applications of a particular control technique that can be used to very effi... more This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control method is adapted from one developed by Hayes, Grebogi, and Ott, and the resulting (stabilized) orbits are known as cupolets (Chaotic, Unstable, Periodic, Orbit-LETS). Cupolets exhibit the interesting property that a given set of controls will uniquely identify a cupolet, independent of its initial condition. Practical applications of cupolets already include data compression, secure communication, and image processing. We demonstrate how cupolets from two interacting chaotic systems may be induced into a state of mutual and self-sustaining stabilization, in a manner that may be an analog of quantum entanglement.
In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a stat... more In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system’s many unstable periodic orbits (generally located densely on the associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero when each system collapses onto a given period orbit. In this paper, we discuss the role that entropy plays in chaotic entanglement. We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved p...
We examine the quantum-classical correspondence from a classical perspective by discussing the po... more We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are convention...
This paper discusses applications of a particular control technique that can be used to very effi... more This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control method is adapted from one developed by Hayes, Grebogi, and Ott, and the resulting (stabilized) orbits are known as cupolets (Chaotic, Unstable, Periodic, Orbit-LETS). Cupolets exhibit the interesting property that a given set of controls will uniquely identify a cupolet, independent of its initial condition. Practical applications of cupolets already include data compression, secure communication, and image processing. We demonstrate how cupolets from two interacting chaotic systems may be induced into a state of mutual and self-sustaining stabilization, in a manner that may be an analog of quantum entanglement.
... ( ) n jb n n jb n n n DFD e DF D FD a F F e DFD FD DFD ∗ ∗ − ∗ − s s ⊙ ⊙ (9 ) ... ( ) ( ) ( 2... more ... ( ) n jb n n jb n n n DFD e DF D FD a F F e DFD FD DFD ∗ ∗ − ∗ − s s ⊙ ⊙ (9 ) ... ( ) ( ) ( 2Re ( ) ( ) jb n n jb n n jb n n jb n n jb n n e DF D FD e DFD FD e DF D FD e DF D FD e DF D FD ∗ − − ∗ − ...
A new formulation of string theory that is applicable to curved target spaces will be developed. ... more A new formulation of string theory that is applicable to curved target spaces will be developed. The observables in the new formulation represent the deformations of the image surface. The path integral is ‘‘gauge fixed,’’ but it retains a global gauge invariance. A measure for the embedding integration is developed which encodes a new geometric regularization procedure. The formulation can
Chaos: An Interdisciplinary Journal of Nonlinear Science
This paper reports the first finding of cupolets in a chaotic Hindmarsh–Rose neural model. Cupole... more This paper reports the first finding of cupolets in a chaotic Hindmarsh–Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh–Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function rN(x). We report the discovery of many cupolets with...
Recent work has highlighted the vast array of dynamics possible within both neuronal networks and... more Recent work has highlighted the vast array of dynamics possible within both neuronal networks and individual neural models. In this work, we demonstrate the capability of interacting chaotic Hindmarsh–Rose neurons to communicate and transition into periodic dynamics through specific interactions which we call mutual stabilization, despite individual units existing in chaotic parameter regimes. Mutual stabilization has been seen before in other chaotic systems but has yet to be reported in interacting neural models. The process of chaotic stabilization is similar to related previous work, where a control scheme which provides small perturbations on carefully chosen Poincaré surfaces that act as control planes stabilized a chaotic trajectory onto a cupolet. For mutual stabilization to occur, the symbolic dynamics of a cupolet are passed through an interaction function such that the output acts as a control on a second chaotic system. If chosen correctly, the second system stabilizes o...
Benefits of interdisciplinary student participation in a university's entrepreneurial activities ... more Benefits of interdisciplinary student participation in a university's entrepreneurial activities are well known. Still, institutional barriers (structural, temporal, spatial, economic, attitudinal) conspire to block participation. Aided by the NSF's Pathways to Innovation Program, the authors conducted a field experiment to increase STEM student participation in a high-profile business proposal competition (BPC). The experiment employed two interventions: informal social networks and bricolage-the innovative and parsimonious use of existing resources. Utilizing these interventions, the authors collaborated to innovatively exploit the Business College's BPC and Engineering College's capstone engineering projects course (CEP). The goal was to facilitate and track STEM students' BPC participation. Participation was voluntary, and not graded. Participation in the BPC increased from 10 STEM students to 27 and the number of BPC finalists increased from 1 STEM-business interdisciplinary team to 4 following the intervention. Findings demonstrate that social network and bricolage-inspired intervention appear useful in increasing STEM student and interdisciplinary team BPC participation and success.
We consider the quantum-classical correspondence from a classical perspective by discussing the p... more We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system's set of cupolets, which are essentially highly-accurate stabilizations of its unstable periodic orbits. The discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external intervention. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. In this paper, we further describe chaotic entanglement and go on to discuss the capacity for chaotic systems to exhibit other characteristic...
This paper discusses applications of a particular control technique that can be used to very effi... more This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control method is adapted from one developed by Hayes, Grebogi, and Ott, and the resulting (stabilized) orbits are known as cupolets (Chaotic, Unstable, Periodic, Orbit-LETS). Cupolets exhibit the interesting property that a given set of controls will uniquely identify a cupolet, independent of its initial condition. Practical applications of cupolets already include data compression, secure communication, and image processing. We demonstrate how cupolets from two interacting chaotic systems may be induced into a state of mutual and self-sustaining stabilization, in a manner that may be an analog of quantum entanglement.
In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a stat... more In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system’s many unstable periodic orbits (generally located densely on the associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero when each system collapses onto a given period orbit. In this paper, we discuss the role that entropy plays in chaotic entanglement. We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved p...
We examine the quantum-classical correspondence from a classical perspective by discussing the po... more We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are convention...
This paper discusses applications of a particular control technique that can be used to very effi... more This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control method is adapted from one developed by Hayes, Grebogi, and Ott, and the resulting (stabilized) orbits are known as cupolets (Chaotic, Unstable, Periodic, Orbit-LETS). Cupolets exhibit the interesting property that a given set of controls will uniquely identify a cupolet, independent of its initial condition. Practical applications of cupolets already include data compression, secure communication, and image processing. We demonstrate how cupolets from two interacting chaotic systems may be induced into a state of mutual and self-sustaining stabilization, in a manner that may be an analog of quantum entanglement.
... ( ) n jb n n jb n n n DFD e DF D FD a F F e DFD FD DFD ∗ ∗ − ∗ − s s ⊙ ⊙ (9 ) ... ( ) ( ) ( 2... more ... ( ) n jb n n jb n n n DFD e DF D FD a F F e DFD FD DFD ∗ ∗ − ∗ − s s ⊙ ⊙ (9 ) ... ( ) ( ) ( 2Re ( ) ( ) jb n n jb n n jb n n jb n n jb n n e DF D FD e DFD FD e DF D FD e DF D FD e DF D FD ∗ − − ∗ − ...
A new formulation of string theory that is applicable to curved target spaces will be developed. ... more A new formulation of string theory that is applicable to curved target spaces will be developed. The observables in the new formulation represent the deformations of the image surface. The path integral is ‘‘gauge fixed,’’ but it retains a global gauge invariance. A measure for the embedding integration is developed which encodes a new geometric regularization procedure. The formulation can
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Papers by Kevin Short