scholarly journals Saddles, arrows, and spirals: Deterministic trajectories in cyclic competition of four species

2011 ◽  
Vol 83 (5) ◽  
Author(s):  
C. H. Durney ◽  
S. O. Case ◽  
M. Pleimling ◽  
R. K. P. Zia
Keyword(s):  
Deterministic Trajectories

Solving the Hamilton-Jacobi-Bellman equation of stochastic control by a semigroup perturbation method

1984 ◽  
Vol 16 (1) ◽  
pp. 16-16
Author(s):  
Domokos Vermes
Keyword(s):  
Bellman Equation ◽  
Value Function ◽  
Sufficient Optimality Condition ◽  
Hamilton Jacobi Bellman Equation ◽  
Deterministic Processes ◽  
Random Jumps ◽  
Hamilton Jacobi Bellman ◽  
Necessary And Sufficient ◽  
The Value Function ◽  
Deterministic Trajectories

We consider the optimal control of deterministic processes with countably many (non-accumulating) random iumps. A necessary and sufficient optimality condition can be given in the form of a Hamilton-jacobi-Bellman equation which is a functionaldifferential equation with boundary conditions in the case considered. Its solution, the value function, is continuously differentiable along the deterministic trajectories if. the random jumps only are controllable and it can be represented as a supremum of smooth subsolutions in the general case, i.e. when both the deterministic motion and the random jumps are controlled (cf. the survey by M. H. A. Davis (p.14)).

Stochastic Generation and Deformation of Toroidal Oscillations in Neuron Model

2018 ◽  
Vol 28 (06) ◽  
pp. 1850070 ◽  
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko ◽  
Evdokia Slepukhina
Keyword(s):  
Neuron Model ◽  
Confidence Regions ◽  
Time Interval ◽  
Dynamical Structure ◽  
Deterministic System ◽  
Phase Duration ◽  
Stochastic Generation ◽  
Stochastic Sensitivity ◽  
Power Spectral ◽  
Deterministic Trajectories

The stochastic Hindmarsh–Rose neuron model in the parametric regions of complex nonlinear dynamics with quiescent and torus bursting regimes is studied. We show that in the zone where the deterministic system exhibits the quiescence, noise can lead to the generation of toroidal dynamical structure with the transition to the bursting regime. The studies of dispersion of random trajectories as well as power spectral density and interspike intervals distribution confirm these changes in system dynamics. Moreover, the stochastic emergence of torus is followed by the noise-induced chaotization. We show that the generation of the torus bursting oscillations is associated with the specificity of the arrangement of deterministic trajectories in the vicinity of the equilibrium as well as its stochastic sensitivity. A probabilistic mechanism of the stochastic generation of torus is investigated on the basis of the analysis of the stochastic sensitivity and geometry of confidence regions. We also show that in the parametric range of the torus bursting, noise can lead to the increase of number of bursts per time interval and to the reduction of spiking and quiescent phase duration.

scholarly journals Relativistically invariant Bohmian trajectories of photons

2021 ◽  
Author(s):  
Joshua Foo ◽  
Estelle Asmodelle ◽  
Austin Lund ◽  
Timothy Ralph
Keyword(s):  
Bohmian Mechanics ◽  
Quantum Mechanical ◽  
Relativistic Velocity ◽  
Weak Measurements ◽  
Hidden Variable ◽  
Bohmian Trajectories ◽  
Velocity Addition ◽  
Velocity Equation ◽  
Interpretation Of Quantum Theory ◽  
Deterministic Trajectories

Abstract Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here we derive expressions for the relativistic velocity and spacetime trajectories of photons in a Michelson-Sagnac-type interferometer. The trajectories satisfy quantum-mechanical continuity, the relativistic velocity addition rule. Our new velocity equation can be operationally defined in terms of weak measurements of momentum and energy. We finally propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.

scholarly journals Experimental Comparison of Bohm-like Theories with Different Primary Ontologies

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 365
Author(s):  
Arthur O. T. Pang ◽  
Hugo Ferretti ◽  
Noah Lupu-Gladstein ◽  
Weng-Kian Tham ◽  
Aharon Brodutch ◽  
...  
Keyword(s):  
Momentum Space ◽  
Particle Dynamics ◽  
Experimental Comparison ◽  
Interpretation Of Quantum Mechanics ◽  
Coherent Light ◽  
Space Dynamics ◽  
Similar Theory ◽  
Deterministic Trajectories ◽  
Slit Experiment ◽  
De Broglie Bohm

The de Broglie-Bohm theory is a hidden-variable interpretation of quantum mechanics which involves particles moving through space along deterministic trajectories. This theory singles out position as the primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum-space, and momentum is singled out as the primary ontological variable. In this paper, we construct the putative particle trajectories for a two-slit experiment in both the position and momentum-space theories by simulating particle dynamics with coherent light. Using a method for constructing trajectories in the primary and non-primary spaces, we compare the phase-space dynamics offered by the two theories and show that they do not agree. This contradictory behaviour underscores the difficulty of selecting one picture of reality from the infinite number of possibilities offered by Bohm-like theories.

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