automata 

hybrid automata 
Automata that may contain differential equations in the discrete states. 

I/O automata 
Automata where connections between subsystems define input/output relations. 

linear hybrid automata 
Automata where the continuous components can change only linearly, and all terms used must be linear. 

rectangular automata 
An automata with each
continuous variable, x, being part of a differential inclusion, i.e.,
satisfying a differential equation of the form a < dx/dt < b,
where a and b are rational constants. 

timed automata 
Automata that may contain
clocks in the discrete states. The value of a clock may be reset as part
of a state transition action. 
  
bond graphs 

hybrid bond graphs 
Bond graphs that contain junctions that act as ideal switches and that are controlled by local finite state machines. 

switched bond graphs 
Bond graphs extended with an ideal switch element. 
  
chattering 
Repeated switching between
two modes of continuous operation. 
  
clock 
A continuous variable
that changes with a constant rate. 
  
complementarity models 
Models with a differential equation part and switching conditions of the form x>=0, y>=0, x*y=0. For example, used in multibody dynamics to model contact constraints (either normal force, N>=0 and separation, d=0, or N=0 and d>=0). 
  
event 

state event 
An event that is
detected. 

step event 
An event that occurs at
a completed numerical integration step. 

time event 
An event that has a
time of occurrence that can be predicted. 
  
event iteration 
The processing of a sequence of consecutive discrete events. 
  
hybrid 

modeling 
The modeling of a physical system by means of a hybrid formalism. 

simulation 
Behavior generation of a hybrid system. 

system 
A model specified by a hybrid formalism. 
  
ideal switch 
Element with two constituent equations (in complementarity form), x>=0,y>=0, x*y=0, and variable causality. 
  
impulse space 
Space in which discontinuous changes in continuous state variables occur. 
  
instantaneous equation 
Equation that determines the posteriori value of a continuous variable at a discontinuity. 
  
jump space 
See impulse space. 
  
limit cycle 
Behavior that
cycles through a sequence of modes in continuous time. 
  
mode 
A system configuration
of continuous operation. 

mythical mode 
A mode that is entered with variable values that cause an immediate further mode transition. 
  
Petri nets 

batch nets 
Extend hybrid Petri nets with a new kind of batch places and batch transitions. 

DAEPetri nets 
Focuses on the interaction between a Petri net model and a continuous model which is a set of Differential Algebraic Equations (DAE). It can be seen as an extension of hybrid automata. 

differential Petri nets 
Introduces the differential place (whose marking may also be negative) and the differential transition and can integrate all kinds of discrete Petri nets. 

firstorder hybrid Petri nets 
Consist of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and either discrete or continuous transitions. The continuous flows have constant rates and the fluid content of each continuous place varies linearly with time. 

fluid stochastic Petri nets 
Extend stochastic Petri nets by introducing places with continuous tokens and arcs with fluid flow so as to handle stochastic fluid flow systems. No continuous transitions are present in this model. 

highlevel hybrid nets 
Nets characterized by the use of structured individual tokens. 

hybrid flow nets 
Consist of a continuous flow net interacting with a Petri net according to a control interaction, i.e., the Petri net controls the continuous flow net and vice versa. 

hybrid Petri nets 
Consist of a "continuous part" (continuous places and transitions) and a "discrete part" (discrete places and transitions). 
  
pinnacle 
A point in behavior evolution that is achieved in a mode that is only active at a point in time. 
  
variable causality 
Variables that dynamically change their character. For example, the variables of an ideal switch may change from input to output and vice versa. 
  
Zenoness 
Characterizes
system behavior that can reach and exceed any point in time. NonZeno behavior
may converge to a limit point, e.g., by advancing time over an interval of
half the size of the previous interval. In Zeno's Paradox Achilles fails to catch a turtoise because every time he reaches its position, the turtoise has moved some as well. 