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Quickstart

  • Installation
  • Simulating a Brain Dynamics Model
  • Training a Brain Dynamics Model
  • Analyzing a Brain Dynamics Model

Tutorials

  • Core Concepts
    • Concept 1: Object-oriented Transformation
    • Concept 2: Dynamical System
  • BDP Tutorials
    • Math Foundation
      • Variable and BrainPyObject
      • Control Flows for JIT compilation
      • NumPy-like Operations
      • Dedicated Operators
    • Model Building
      • Using Built-in Models
      • Building Conductance-based Neuron Models
      • Phenomenological Synaptic Models
      • Kinetic Synaptic Models
      • Building Network Models
      • Customizing Your Neuron Models
      • Customizing Your Synapse Models
      • How to customize a synapse
    • Model Simulation
      • Simulation with DSRunner
      • Parallel Simulation for Parameter Exploration
    • Model Training
      • Building Training Models
      • Training with Offline Algorithms
      • Training with Online Algorithms
      • Training with Back-propagation Algorithms
      • Introduction to Echo State Network
    • Model Analysis
      • Low-dimensional Analyzers
      • High-dimensional Analyzers
      • Analysis of a Decision-making Model
  • BDP Toolboxes
    • Numerical Solvers for Ordinary Differential Equations
    • Numerical Solvers for Stochastic Differential Equations
    • Numerical Solvers for Fractional Differential Equations
    • Numerical Solvers for Delay Differential Equations
    • Joint Differential Equations
    • Synaptic Connections
    • Synaptic Weights
    • Gradient Descent Optimizers
    • Saving and Loading
    • Surrogate gradient
    • Inputs Construction
  • Advanced Tutorials
    • Advanced Math
      • JIT Compilation with BrainPyObject
      • Automatic Differentiation with BrainPyObject
    • Interoperation
      • Use Flax modules as a part of the BrainPy program
      • Integrate BrainPy models into Flax (Example 1)
      • Integrate BrainPy Models into Flax (Example 2)
    • Brain Dynamics Dedicated Operators
      • Low-level Operator Customization
    • Developer Guides
      • Contributing to BrainPy
    • Others
      • How does low-dimensional analyzers work?
  • Frequently Asked Questions
    • How to debug in BrainPy
    • Gotchas of BrainPy Transformations
    • How to cite BrainPy?
    • How is brainpy different from other frameworks?
    • BrainPy Ecosystem for Brain Dynamics Modeling
  • API Documentation
    • Release notes (brainpy)
    • brainpy module
      • Integrator
      • JointEq
      • IntegratorRunner
      • odeint
      • sdeint
      • fdeint
      • DynamicalSystem
      • DynSysGroup
      • Sequential
      • Network
      • Dynamic
      • Projection
      • DSRunner
      • DSTrainer
      • BPTT
      • BPFF
      • OnlineTrainer
      • ForceTrainer
      • OfflineTrainer
      • RidgeTrainer
      • LoopOverTime
    • brainpy.math module
      • BrainPyObject
      • FunAsObject
      • Partial
      • NodeList
      • NodeDict
      • node_dict
      • node_list
      • Variable
      • Parameter
      • TrainVar
      • VariableView
      • VarList
      • VarDict
      • var_list
      • var_dict
      • grad
      • vector_grad
      • jacobian
      • jacrev
      • jacfwd
      • hessian
      • make_loop
      • make_while
      • make_cond
      • cond
      • ifelse
      • for_loop
      • while_loop
      • jit
      • cls_jit
      • to_object
      • function
      • set
      • set_environment
      • set_float
      • get_float
      • set_int
      • get_int
      • set_bool
      • get_bool
      • set_complex
      • get_complex
      • set_dt
      • get_dt
      • set_mode
      • get_mode
      • enable_x64
      • disable_x64
      • set_platform
      • get_platform
      • set_host_device_count
      • clear_buffer_memory
      • enable_gpu_memory_preallocation
      • disable_gpu_memory_preallocation
      • ditype
      • dftype
      • environment
      • batching_environment
      • training_environment
      • as_device_array
      • as_jax
      • as_ndarray
      • as_numpy
      • as_variable
      • pre2post_sum
      • pre2post_prod
      • pre2post_max
      • pre2post_min
      • pre2post_mean
      • pre2post_event_sum
      • pre2post_csr_event_sum
      • pre2post_coo_event_sum
      • pre2syn
      • syn2post_sum
      • syn2post
      • syn2post_prod
      • syn2post_max
      • syn2post_min
      • syn2post_mean
      • syn2post_softmax
      • celu
      • elu
      • gelu
      • glu
      • prelu
      • silu
      • selu
      • relu
      • relu6
      • rrelu
      • hard_silu
      • leaky_relu
      • hard_tanh
      • hard_sigmoid
      • tanh_shrink
      • hard_swish
      • hard_shrink
      • soft_sign
      • soft_shrink
      • softmax
      • softmin
      • softplus
      • swish
      • mish
      • log_sigmoid
      • log_softmax
      • one_hot
      • normalize
      • sigmoid
      • identity
      • tanh
      • TimeDelay
      • LengthDelay
      • NeuTimeDelay
      • NeuLenDelay
      • ROTATE_UPDATE
      • CONCAT_UPDATE
      • Mode
      • NonBatchingMode
      • BatchingMode
      • TrainingMode
      • nonbatching_mode
      • batching_mode
      • training_mode
      • csrmv
      • coomv
      • seg_matmul
      • csr_to_dense
      • csr_to_coo
      • coo_to_csr
      • csrmv
      • info
      • event_mv_prob_homo
      • event_mv_prob_uniform
      • event_mv_prob_normal
      • mv_prob_homo
      • mv_prob_uniform
      • mv_prob_normal
      • brainpy.math.surrogate.Surrogate
      • brainpy.math.surrogate.Sigmoid
      • brainpy.math.surrogate.sigmoid
      • brainpy.math.surrogate.PiecewiseQuadratic
      • brainpy.math.surrogate.piecewise_quadratic
      • brainpy.math.surrogate.PiecewiseExp
      • brainpy.math.surrogate.piecewise_exp
      • brainpy.math.surrogate.SoftSign
      • brainpy.math.surrogate.soft_sign
      • brainpy.math.surrogate.Arctan
      • brainpy.math.surrogate.arctan
      • brainpy.math.surrogate.NonzeroSignLog
      • brainpy.math.surrogate.nonzero_sign_log
      • brainpy.math.surrogate.ERF
      • brainpy.math.surrogate.erf
      • brainpy.math.surrogate.PiecewiseLeakyRelu
      • brainpy.math.surrogate.piecewise_leaky_relu
      • brainpy.math.surrogate.SquarewaveFourierSeries
      • brainpy.math.surrogate.squarewave_fourier_series
      • brainpy.math.surrogate.S2NN
      • brainpy.math.surrogate.s2nn
      • brainpy.math.surrogate.QPseudoSpike
      • brainpy.math.surrogate.q_pseudo_spike
      • brainpy.math.surrogate.LeakyRelu
      • brainpy.math.surrogate.leaky_relu
      • brainpy.math.surrogate.LogTailedRelu
      • brainpy.math.surrogate.log_tailed_relu
      • brainpy.math.surrogate.ReluGrad
      • brainpy.math.surrogate.relu_grad
      • brainpy.math.surrogate.GaussianGrad
      • brainpy.math.surrogate.gaussian_grad
      • brainpy.math.surrogate.InvSquareGrad
      • brainpy.math.surrogate.inv_square_grad
      • brainpy.math.surrogate.MultiGaussianGrad
      • brainpy.math.surrogate.multi_gaussian_grad
      • brainpy.math.surrogate.SlayerGrad
      • brainpy.math.surrogate.slayer_grad
      • brainpy.math.surrogate.inv_square_grad2
      • brainpy.math.surrogate.relu_grad2
      • seed
      • split_key
      • split_keys
      • default_rng
      • rand
      • randint
      • random_integers
      • randn
      • random
      • random_sample
      • ranf
      • sample
      • choice
      • permutation
      • shuffle
      • beta
      • exponential
      • gamma
      • gumbel
      • laplace
      • logistic
      • normal
      • pareto
      • poisson
      • standard_cauchy
      • standard_exponential
      • standard_gamma
      • standard_normal
      • standard_t
      • uniform
      • truncated_normal
      • bernoulli
      • lognormal
      • binomial
      • chisquare
      • dirichlet
      • geometric
      • f
      • hypergeometric
      • logseries
      • multinomial
      • multivariate_normal
      • negative_binomial
      • noncentral_chisquare
      • noncentral_f
      • power
      • rayleigh
      • triangular
      • vonmises
      • wald
      • weibull
      • weibull_min
      • zipf
      • maxwell
      • t
      • orthogonal
      • loggamma
      • categorical
      • rand_like
      • randint_like
      • randn_like
      • RandomState
      • Generator
      • DEFAULT
      • cholesky
      • cond
      • det
      • eig
      • eigh
      • eigvals
      • eigvalsh
      • inv
      • svd
      • lstsq
      • matrix_power
      • matrix_rank
      • norm
      • pinv
      • qr
      • solve
      • slogdet
      • tensorinv
      • tensorsolve
      • multi_dot
      • fft
      • fft2
      • fftfreq
      • fftn
      • fftshift
      • hfft
      • ifft
      • ifft2
      • ifftn
      • ifftshift
      • ihfft
      • irfft
      • irfft2
      • irfftn
      • rfft
      • rfft2
      • rfftfreq
      • rfftn
    • brainpy.dnn module
      • Activation
      • Flatten
      • FunAsLayer
      • Threshold
      • ReLU
      • RReLU
      • Hardtanh
      • ReLU6
      • Sigmoid
      • Hardsigmoid
      • Tanh
      • SiLU
      • Mish
      • Hardswish
      • ELU
      • CELU
      • SELU
      • GLU
      • GELU
      • Hardshrink
      • LeakyReLU
      • LogSigmoid
      • Softplus
      • Softshrink
      • PReLU
      • Softsign
      • Tanhshrink
      • Softmin
      • Softmax
      • Softmax2d
      • LogSoftmax
      • Conv1d
      • Conv2d
      • Conv3d
      • Conv1D
      • Conv2D
      • Conv3D
      • ConvTranspose1d
      • ConvTranspose2d
      • ConvTranspose3d
      • Dense
      • Linear
      • Identity
      • AllToAll
      • OneToOne
      • MaskedLinear
      • CSRLinear
      • EventCSRLinear
      • JitFPHomoLinear
      • JitFPUniformLinear
      • JitFPNormalLinear
      • EventJitFPHomoLinear
      • EventJitFPNormalLinear
      • EventJitFPUniformLinear
      • BatchNorm1d
      • BatchNorm2d
      • BatchNorm3d
      • BatchNorm1D
      • BatchNorm2D
      • BatchNorm3D
      • LayerNorm
      • GroupNorm
      • InstanceNorm
      • MaxPool
      • MaxPool1d
      • MaxPool2d
      • MaxPool3d
      • MinPool
      • AvgPool
      • AvgPool1d
      • AvgPool2d
      • AvgPool3d
      • AdaptiveAvgPool1d
      • AdaptiveAvgPool2d
      • AdaptiveAvgPool3d
      • AdaptiveMaxPool1d
      • AdaptiveMaxPool2d
      • AdaptiveMaxPool3d
      • FromFlax
      • ToFlaxRNNCell
      • ToFlax
      • Layer
      • Dropout
      • Activation
      • Flatten
      • FunAsLayer
    • brainpy.dyn module
      • Base Classes
        • NeuDyn
        • SynDyn
        • IonChaDyn
      • Ion Dynamics
        • mix_ions
        • Ion
        • MixIons
        • Calcium
        • CalciumFixed
        • CalciumDetailed
        • CalciumFirstOrder
        • Sodium
        • SodiumFixed
        • Potassium
        • PotassiumFixed
      • Ion Channel Dynamics
        • IonChannel
        • CalciumChannel
        • ICaN_IS2008
        • ICaT_HM1992
        • ICaT_HP1992
        • ICaHT_HM1992
        • ICaHT_Re1993
        • ICaL_IS2008
        • PotassiumChannel
        • IKDR_Ba2002v2
        • IK_TM1991v2
        • IK_HH1952v2
        • IKA1_HM1992v2
        • IKA2_HM1992v2
        • IKK2A_HM1992v2
        • IKK2B_HM1992v2
        • IKNI_Ya1989v2
        • IK_Leak
        • IKDR_Ba2002
        • IK_TM1991
        • IK_HH1952
        • IKA1_HM1992
        • IKA2_HM1992
        • IKK2A_HM1992
        • IKK2B_HM1992
        • IKNI_Ya1989
        • IKL
        • SodiumChannel
        • INa_Ba2002
        • INa_TM1991
        • INa_HH1952
        • INa_Ba2002v2
        • INa_TM1991v2
        • INa_HH1952v2
        • Ih_HM1992
        • Ih_De1996
        • IAHP_De1994v2
        • IAHP_De1994
        • LeakyChannel
        • IL
      • Neuron Dynamics
        • Lif
        • LifLTC
        • LifRefLTC
        • LifRef
        • ExpIF
        • ExpIFLTC
        • ExpIFRefLTC
        • ExpIFRef
        • AdExIF
        • AdExIFLTC
        • AdExIFRefLTC
        • AdExIFRef
        • QuaIF
        • QuaIFLTC
        • QuaIFRefLTC
        • QuaIFRef
        • AdQuaIF
        • AdQuaIFLTC
        • AdQuaIFRefLTC
        • AdQuaIFRef
        • Gif
        • GifLTC
        • GifRefLTC
        • GifRef
        • Izhikevich
        • IzhikevichLTC
        • IzhikevichRefLTC
        • IzhikevichRef
        • HHTypedNeuron
        • CondNeuGroupLTC
        • CondNeuGroup
        • HH
        • HHLTC
        • MorrisLecar
        • MorrisLecarLTC
        • WangBuzsakiHH
        • WangBuzsakiHHLTC
        • HHTypedNeuron
        • CondNeuGroupLTC
        • CondNeuGroup
        • HH
        • HHLTC
        • MorrisLecar
        • MorrisLecarLTC
        • WangBuzsakiHH
        • WangBuzsakiHHLTC
      • Synaptic Dynamics
        • Delta
        • Expon
        • Alpha
        • DualExpon
        • DualExponV2
        • NMDA
        • STD
        • STP
        • AMPA
        • GABAa
        • BioNMDA
        • DiffusiveCoupling
        • AdditiveCoupling
      • Synaptic Outputs
        • SynOut
        • COBA
        • CUBA
        • MgBlock
      • Firing Rate Models
        • FHN
        • FeedbackFHN
        • QIF
        • StuartLandauOscillator
        • WilsonCowanModel
        • ThresholdLinearModel
        • RNNCell
        • GRUCell
        • LSTMCell
        • Conv1dLSTMCell
        • Conv2dLSTMCell
        • Conv3dLSTMCell
        • NVAR
        • Reservoir
      • Synaptic Projections
        • ProjAlignPostMg1
        • ProjAlignPostMg2
        • ProjAlignPost1
        • ProjAlignPost2
        • ProjAlignPreMg1
        • ProjAlignPreMg2
        • ProjAlignPre1
        • ProjAlignPre2
        • VanillaProj
        • SynConn
        • PoissonInput
        • InputVar
      • Synaptic Plasticity
        • STDP_Song2000
      • Common Dynamical Models
        • Leaky
        • Integrator
        • InputGroup
        • OutputGroup
        • SpikeTimeGroup
        • PoissonGroup
        • OUProcess
    • brainpy.integrators module
      • ODEIntegrator
      • set_default_odeint
      • get_default_odeint
      • register_ode_integrator
      • get_supported_methods
      • ExplicitRKIntegrator
      • Euler
      • MidPoint
      • Heun2
      • Ralston2
      • RK2
      • RK3
      • Heun3
      • Ralston3
      • SSPRK3
      • RK4
      • Ralston4
      • RK4Rule38
      • AdaptiveRKIntegrator
      • RKF12
      • RKF45
      • DormandPrince
      • CashKarp
      • BogackiShampine
      • HeunEuler
      • ExponentialEuler
      • SDEIntegrator
      • set_default_sdeint
      • get_default_sdeint
      • register_sde_integrator
      • get_supported_methods
      • Euler
      • Heun
      • Milstein
      • MilsteinGradFree
      • ExponentialEuler
      • SRK1W1
      • SRK2W1
      • KlPl
      • FDEIntegrator
      • set_default_fdeint
      • get_default_fdeint
      • register_fde_integrator
      • get_supported_methods
      • CaputoEuler
      • CaputoL1Schema
      • GLShortMemory
    • brainpy.analysis module
      • PhasePlane1D
      • PhasePlane2D
      • Bifurcation1D
      • Bifurcation2D
      • FastSlow1D
      • FastSlow2D
      • SlowPointFinder
    • brainpy.connect module
      • set_default_dtype
      • mat2coo
      • mat2csc
      • mat2csr
      • csr2csc
      • csr2mat
      • csr2coo
      • coo2csr
      • coo2csc
      • coo2mat
      • coo2mat_num
      • mat2mat_num
      • visualizeMat
      • Connector
      • TwoEndConnector
      • OneEndConnector
      • CONN_MAT
      • PRE_IDS
      • POST_IDS
      • PRE2POST
      • POST2PRE
      • PRE2SYN
      • POST2SYN
      • MatConn
      • IJConn
      • CSRConn
      • SparseMatConn
      • FixedProb
      • FixedPreNum
      • FixedPostNum
      • FixedTotalNum
      • GaussianProb
      • ProbDist
      • SmallWorld
      • ScaleFreeBA
      • ScaleFreeBADual
      • PowerLaw
      • One2One
      • All2All
      • GridFour
      • GridEight
      • GridN
      • one2one
      • all2all
      • grid_four
      • grid_eight
    • brainpy.encoding module
      • Encoder
      • LatencyEncoder
      • WeightedPhaseEncoder
      • PoissonEncoder
      • DiffEncoder
    • brainpy.initialize module
      • Initializer
      • ZeroInit
      • Constant
      • OneInit
      • Identity
      • Normal
      • Uniform
      • VarianceScaling
      • KaimingUniform
      • KaimingNormal
      • XavierUniform
      • XavierNormal
      • LecunUniform
      • LecunNormal
      • Orthogonal
      • DeltaOrthogonal
      • GaussianDecay
      • DOGDecay
    • brainpy.inputs module
      • brainpy.inputs.section_input
      • brainpy.inputs.constant_input
      • brainpy.inputs.spike_input
      • brainpy.inputs.ramp_input
      • brainpy.inputs.wiener_process
      • brainpy.inputs.ou_process
      • brainpy.inputs.sinusoidal_input
      • brainpy.inputs.square_input
    • brainpy.losses module
      • cross_entropy_loss
      • cross_entropy_sparse
      • cross_entropy_sigmoid
      • nll_loss
      • l1_loss
      • l2_loss
      • huber_loss
      • mean_absolute_error
      • mean_squared_error
      • mean_squared_log_error
      • binary_logistic_loss
      • multiclass_logistic_loss
      • sigmoid_binary_cross_entropy
      • softmax_cross_entropy
      • log_cosh_loss
      • ctc_loss_with_forward_probs
      • ctc_loss
      • CrossEntropyLoss
      • NLLLoss
      • L1Loss
      • MAELoss
      • MSELoss
      • l2_norm
      • mean_absolute
      • mean_square
      • log_cosh
      • smooth_labels
    • brainpy.measure module
      • cross_correlation
      • voltage_fluctuation
      • matrix_correlation
      • weighted_correlation
      • functional_connectivity
      • raster_plot
      • firing_rate
      • unitary_LFP
    • brainpy.optim module
      • Optimizer
      • SGD
      • Momentum
      • MomentumNesterov
      • Adagrad
      • Adadelta
      • RMSProp
      • Adam
      • LARS
      • Adan
      • AdamW
      • make_schedule
      • Scheduler
      • Constant
      • StepLR
      • MultiStepLR
      • CosineAnnealingLR
      • CosineAnnealingWarmRestarts
      • ExponentialLR
      • ExponentialDecayLR
      • ExponentialDecay
      • InverseTimeDecayLR
      • InverseTimeDecay
      • PolynomialDecayLR
      • PolynomialDecay
      • PiecewiseConstantLR
      • PiecewiseConstant
    • brainpy.running module
      • jax_vectorize_map
      • jax_parallelize_map
      • process_pool
      • process_pool_lock
      • cpu_ordered_parallel
      • cpu_unordered_parallel
    • brainpy.mixin module
      • MixIn
      • AlignPost
      • ParamDesc
      • ParamDescInit
      • BindCondData
      • Container
      • TreeNode
      • JointType
    • brainpy.channels module
    • brainpy.neurons module
      • brainpy.neurons.HH
      • brainpy.neurons.MorrisLecar
      • brainpy.neurons.PinskyRinzelModel
      • brainpy.neurons.WangBuzsakiModel
      • brainpy.neurons.FractionalNeuron
      • brainpy.neurons.FractionalFHR
      • brainpy.neurons.FractionalIzhikevich
      • brainpy.neurons.LeakyIntegrator
      • brainpy.neurons.LIF
      • brainpy.neurons.ExpIF
      • brainpy.neurons.AdExIF
      • brainpy.neurons.QuaIF
      • brainpy.neurons.AdQuaIF
      • brainpy.neurons.GIF
      • brainpy.neurons.Izhikevich
      • brainpy.neurons.HindmarshRose
      • brainpy.neurons.FHN
      • brainpy.neurons.ALIFBellec2020
      • brainpy.neurons.LIF_SFA_Bellec2020
    • brainpy.rates module
    • brainpy.synapses module
      • brainpy.synapses.Delta
      • brainpy.synapses.Exponential
      • brainpy.synapses.DualExponential
      • brainpy.synapses.Alpha
      • brainpy.synapses.NMDA
      • brainpy.synapses.PoissonInput
      • brainpy.synapses.AMPA
      • brainpy.synapses.GABAa
      • brainpy.synapses.BioNMDA
      • brainpy.synapses.DiffusiveCoupling
      • brainpy.synapses.AdditiveCoupling
      • brainpy.synapses.GapJunction
      • brainpy.synapses.STP
    • brainpy.synouts module
      • brainpy.synouts.COBA
      • brainpy.synouts.CUBA
      • brainpy.synouts.MgBlock
    • brainpy.synplast module
      • brainpy.synplast.STD
      • brainpy.synplast.STP
    • brainpy.layers module
  • .rst

Model Analysis

Model Analysis#

  • Low-dimensional Analyzers
  • High-dimensional Analyzers
  • Analysis of a Decision-making Model

previous

Introduction to Echo State Network

next

Low-dimensional Analyzers

By BrainPy Team

© Copyright 2020-2023, BrainPy.

Last updated on Sep 22, 2023.